# Quizbank/Electricity and Magnetism (calculus based)/c06

calcPhyEMq/c06 ID153287923206 (Study guide)

Exams:

78 Tests = 3 versions x 26 variations: Each of the 26 variations (A, B, ...) represents a different random selection of questions taken from the study guide.The 3 versions (0,1,..) all have the same questions but in different order and with different numerical inputs. Unless all students take version "0" it is best to reserve it for the instructor because the questions are grouped according to the order in which they appear on the study guide.

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### c06 A0

1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?

a) 7.825E+02 N/C
b) 8.607E+02 N/C
c) 9.468E+02 N/C
d) 1.041E+03 N/C
e) 1.146E+03 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

a) 2.964E+00 N/C
b) 3.260E+00 N/C
c) 3.586E+00 N/C
d) 3.944E+00 N/C
e) 4.339E+00 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.1 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.606E+01 N·m2/C
b) 6.167E+01 N·m2/C
c) 6.784E+01 N·m2/C
d) 7.462E+01 N·m2/C
e) 8.208E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

a) 2.067E+03 V·m
b) 2.274E+03 V·m
c) 2.501E+03 V·m
d) 2.752E+03 V·m
e) 3.027E+03 V·m

#### c06 A1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.6 m, z=z0=1.2 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.3m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.809E+01 N·m2/C
b) 5.290E+01 N·m2/C
c) 5.819E+01 N·m2/C
d) 6.401E+01 N·m2/C
e) 7.041E+01 N·m2/C

2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?

a) 2.039E+01 N/C
b) 2.243E+01 N/C
c) 2.467E+01 N/C
d) 2.714E+01 N/C
e) 2.985E+01 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 9.144E+00 N/C
b) 1.006E+01 N/C
c) 1.106E+01 N/C
d) 1.217E+01 N/C
e) 1.339E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m
b) 2.871E+03 V·m
c) 3.158E+03 V·m
d) 3.474E+03 V·m
e) 3.822E+03 V·m

#### c06 A2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.876E+01 N·m2/C
b) 8.664E+01 N·m2/C
c) 9.531E+01 N·m2/C
d) 1.048E+02 N·m2/C
e) 1.153E+02 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

a) 2.067E+03 V·m
b) 2.274E+03 V·m
c) 2.501E+03 V·m
d) 2.752E+03 V·m
e) 3.027E+03 V·m

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?

a) 5.297E+00 N/C
b) 5.827E+00 N/C
c) 6.409E+00 N/C
d) 7.050E+00 N/C
e) 7.755E+00 N/C

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.383E+02 N/C
b) 1.522E+02 N/C
c) 1.674E+02 N/C
d) 1.841E+02 N/C
e) 2.025E+02 N/C

### c06 B0

1) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.123E+02 N/C
b) 1.235E+02 N/C
c) 1.358E+02 N/C
d) 1.494E+02 N/C
e) 1.644E+02 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 5.3m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.793E+01 N·m2/C
b) 8.572E+01 N·m2/C
c) 9.429E+01 N·m2/C
d) 1.037E+02 N·m2/C
e) 1.141E+02 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

a) 7.200E+01 V·m
b) 7.920E+01 V·m
c) 8.712E+01 V·m
d) 9.583E+01 V·m
e) 1.054E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.192E+01 N·m2/C
b) 6.811E+01 N·m2/C
c) 7.492E+01 N·m2/C
d) 8.242E+01 N·m2/C
e) 9.066E+01 N·m2/C

#### c06 B1

1) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.383E+02 N/C
b) 1.522E+02 N/C
c) 1.674E+02 N/C
d) 1.841E+02 N/C
e) 2.025E+02 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.978E+01 N·m2/C
b) 6.576E+01 N·m2/C
c) 7.233E+01 N·m2/C
d) 7.957E+01 N·m2/C
e) 8.752E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

a) 1.997E+03 V·m
b) 2.197E+03 V·m
c) 2.417E+03 V·m
d) 2.659E+03 V·m
e) 2.924E+03 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.1 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.606E+01 N·m2/C
b) 6.167E+01 N·m2/C
c) 6.784E+01 N·m2/C
d) 7.462E+01 N·m2/C
e) 8.208E+01 N·m2/C

#### c06 B2

1) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

a) 3.604E+02 N/C
b) 3.964E+02 N/C
c) 4.360E+02 N/C
d) 4.796E+02 N/C
e) 5.276E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.978E+01 N·m2/C
b) 6.576E+01 N·m2/C
c) 7.233E+01 N·m2/C
d) 7.957E+01 N·m2/C
e) 8.752E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.214E+01 N·m2/C
b) 2.436E+01 N·m2/C
c) 2.679E+01 N·m2/C
d) 2.947E+01 N·m2/C
e) 3.242E+01 N·m2/C

### c06 C0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 16 N/C has components in the y and z directions and is directed at 53° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.420E+01 N·m2/C
b) 4.862E+01 N·m2/C
c) 5.348E+01 N·m2/C
d) 5.882E+01 N·m2/C
e) 6.471E+01 N·m2/C

2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?

a) 2.039E+01 N/C
b) 2.243E+01 N/C
c) 2.467E+01 N/C
d) 2.714E+01 N/C
e) 2.985E+01 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

a) 2.988E+00 N/C
b) 3.287E+00 N/C
c) 3.616E+00 N/C
d) 3.977E+00 N/C
e) 4.375E+00 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 9.823E+00 N·m2/C
b) 1.080E+01 N·m2/C
c) 1.189E+01 N·m2/C
d) 1.307E+01 N·m2/C
e) 1.438E+01 N·m2/C

#### c06 C1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?

a) 9.642E+00 N/C
b) 1.061E+01 N/C
c) 1.167E+01 N/C
d) 1.283E+01 N/C
e) 1.412E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.415E+01 N·m2/C
b) 9.256E+01 N·m2/C
c) 1.018E+02 N·m2/C
d) 1.120E+02 N·m2/C
e) 1.232E+02 N·m2/C

3) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.214E+01 N·m2/C
b) 2.436E+01 N·m2/C
c) 2.679E+01 N·m2/C
d) 2.947E+01 N·m2/C
e) 3.242E+01 N·m2/C

#### c06 C2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.662E+01 N·m2/C
b) 4.028E+01 N·m2/C
c) 4.430E+01 N·m2/C
d) 4.873E+01 N·m2/C
e) 5.361E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.992E+01 N·m2/C
b) 2.192E+01 N·m2/C
c) 2.411E+01 N·m2/C
d) 2.652E+01 N·m2/C
e) 2.917E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 9.144E+00 N/C
b) 1.006E+01 N/C
c) 1.106E+01 N/C
d) 1.217E+01 N/C
e) 1.339E+01 N/C

4) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?

a) 7.825E+02 N/C
b) 8.607E+02 N/C
c) 9.468E+02 N/C
d) 1.041E+03 N/C
e) 1.146E+03 N/C

### c06 D0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.5 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 8.3m2. Those in the xy plane have area 5.7m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.408E+01 N·m2/C
b) 5.949E+01 N·m2/C
c) 6.544E+01 N·m2/C
d) 7.198E+01 N·m2/C
e) 7.918E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

a) 1.128E+04 V·m
b) 1.241E+04 V·m
c) 1.365E+04 V·m
d) 1.502E+04 V·m
e) 1.652E+04 V·m

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?

a) 5.297E+00 N/C
b) 5.827E+00 N/C
c) 6.409E+00 N/C
d) 7.050E+00 N/C
e) 7.755E+00 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.740E+01 N·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C

#### c06 D1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.989E+01 N·m2/C
b) 6.588E+01 N·m2/C
c) 7.247E+01 N·m2/C
d) 7.971E+01 N·m2/C
e) 8.769E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m
b) 7.759E+03 V·m
c) 8.535E+03 V·m
d) 9.388E+03 V·m
e) 1.033E+04 V·m

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?

a) 9.642E+00 N/C
b) 1.061E+01 N/C
c) 1.167E+01 N/C
d) 1.283E+01 N/C
e) 1.412E+01 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.740E+01 N·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C

#### c06 D2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.125E+01 N·m2/C
b) 4.537E+01 N·m2/C
c) 4.991E+01 N·m2/C
d) 5.490E+01 N·m2/C
e) 6.039E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.012E+01 N·m2/C
b) 2.213E+01 N·m2/C
c) 2.435E+01 N·m2/C
d) 2.678E+01 N·m2/C
e) 2.946E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

a) 3.251E+01 N/C
b) 3.577E+01 N/C
c) 3.934E+01 N/C
d) 4.328E+01 N/C
e) 4.760E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

a) 9.952E+03 V·m
b) 1.095E+04 V·m
c) 1.204E+04 V·m
d) 1.325E+04 V·m
e) 1.457E+04 V·m

### c06 E0

1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?

a) 7.825E+02 N/C
b) 8.607E+02 N/C
c) 9.468E+02 N/C
d) 1.041E+03 N/C
e) 1.146E+03 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.695E+01 N·m2/C
b) 4.065E+01 N·m2/C
c) 4.472E+01 N·m2/C
d) 4.919E+01 N·m2/C
e) 5.411E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.270E+01 N·m2/C
b) 6.897E+01 N·m2/C
c) 7.586E+01 N·m2/C
d) 8.345E+01 N·m2/C
e) 9.179E+01 N·m2/C

#### c06 E1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.712E+01 N·m2/C
b) 4.083E+01 N·m2/C
c) 4.491E+01 N·m2/C
d) 4.940E+01 N·m2/C
e) 5.434E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

a) 1.997E+03 V·m
b) 2.197E+03 V·m
c) 2.417E+03 V·m
d) 2.659E+03 V·m
e) 2.924E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.314E+01 N·m2/C
b) 9.146E+01 N·m2/C
c) 1.006E+02 N·m2/C
d) 1.107E+02 N·m2/C
e) 1.217E+02 N·m2/C

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.579E+02 N/C
b) 2.837E+02 N/C
c) 3.121E+02 N/C
d) 3.433E+02 N/C
e) 3.776E+02 N/C

#### c06 E2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.989E+01 N·m2/C
b) 6.588E+01 N·m2/C
c) 7.247E+01 N·m2/C
d) 7.971E+01 N·m2/C
e) 8.769E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.924E+01 N·m2/C
b) 4.316E+01 N·m2/C
c) 4.748E+01 N·m2/C
d) 5.222E+01 N·m2/C
e) 5.745E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m
b) 7.759E+03 V·m
c) 8.535E+03 V·m
d) 9.388E+03 V·m
e) 1.033E+04 V·m

4) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.123E+02 N/C
b) 1.235E+02 N/C
c) 1.358E+02 N/C
d) 1.494E+02 N/C
e) 1.644E+02 N/C

### c06 F0

1) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.123E+02 N/C
b) 1.235E+02 N/C
c) 1.358E+02 N/C
d) 1.494E+02 N/C
e) 1.644E+02 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?

a) 9.592E+00 N/C
b) 1.055E+01 N/C
c) 1.161E+01 N/C
d) 1.277E+01 N/C
e) 1.404E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.777E+01 N·m2/C
b) 5.254E+01 N·m2/C
c) 5.780E+01 N·m2/C
d) 6.358E+01 N·m2/C
e) 6.993E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.924E+01 N·m2/C
b) 4.316E+01 N·m2/C
c) 4.748E+01 N·m2/C
d) 5.222E+01 N·m2/C
e) 5.745E+01 N·m2/C

#### c06 F1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.134E+01 N·m2/C
b) 2.347E+01 N·m2/C
c) 2.582E+01 N·m2/C
d) 2.840E+01 N·m2/C
e) 3.124E+01 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?

a) 6.641E+00 N/C
b) 7.305E+00 N/C
c) 8.036E+00 N/C
d) 8.839E+00 N/C
e) 9.723E+00 N/C

3) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.079E+02 N/C
b) 2.287E+02 N/C
c) 2.516E+02 N/C
d) 2.767E+02 N/C
e) 3.044E+02 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.992E+01 N·m2/C
b) 2.192E+01 N·m2/C
c) 2.411E+01 N·m2/C
d) 2.652E+01 N·m2/C
e) 2.917E+01 N·m2/C

#### c06 F2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.415E+01 N·m2/C
b) 9.256E+01 N·m2/C
c) 1.018E+02 N·m2/C
d) 1.120E+02 N·m2/C
e) 1.232E+02 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 9.144E+00 N/C
b) 1.006E+01 N/C
c) 1.106E+01 N/C
d) 1.217E+01 N/C
e) 1.339E+01 N/C

3) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

a) 3.604E+02 N/C
b) 3.964E+02 N/C
c) 4.360E+02 N/C
d) 4.796E+02 N/C
e) 5.276E+02 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.6 m, z=z0=1.2 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.3m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.809E+01 N·m2/C
b) 5.290E+01 N·m2/C
c) 5.819E+01 N·m2/C
d) 6.401E+01 N·m2/C
e) 7.041E+01 N·m2/C

### c06 G0

1) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C
b) 2.501E+02 N/C
c) 2.751E+02 N/C
d) 3.026E+02 N/C
e) 3.329E+02 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.186E+01 N·m2/C
b) 2.404E+01 N·m2/C
c) 2.645E+01 N·m2/C
d) 2.909E+01 N·m2/C
e) 3.200E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

a) 7.200E+01 V·m
b) 7.920E+01 V·m
c) 8.712E+01 V·m
d) 9.583E+01 V·m
e) 1.054E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.978E+01 N·m2/C
b) 6.576E+01 N·m2/C
c) 7.233E+01 N·m2/C
d) 7.957E+01 N·m2/C
e) 8.752E+01 N·m2/C

#### c06 G1

1) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C
b) 2.501E+02 N/C
c) 2.751E+02 N/C
d) 3.026E+02 N/C
e) 3.329E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m
b) 2.871E+03 V·m
c) 3.158E+03 V·m
d) 3.474E+03 V·m
e) 3.822E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.740E+01 N·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.186E+01 N·m2/C
b) 2.404E+01 N·m2/C
c) 2.645E+01 N·m2/C
d) 2.909E+01 N·m2/C
e) 3.200E+01 N·m2/C

#### c06 G2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 13.0m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 7.0, 5.7) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.953E+01 N·m2/C
b) 5.449E+01 N·m2/C
c) 5.993E+01 N·m2/C
d) 6.593E+01 N·m2/C
e) 7.252E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

a) 1.997E+03 V·m
b) 2.197E+03 V·m
c) 2.417E+03 V·m
d) 2.659E+03 V·m
e) 2.924E+03 V·m

3) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?

a) 4.782E+02 N/C
b) 5.260E+02 N/C
c) 5.787E+02 N/C
d) 6.365E+02 N/C
e) 7.002E+02 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 16 N/C has components in the y and z directions and is directed at 53° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.420E+01 N·m2/C
b) 4.862E+01 N·m2/C
c) 5.348E+01 N·m2/C
d) 5.882E+01 N·m2/C
e) 6.471E+01 N·m2/C

### c06 H0

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

a) 3.337E+03 V·m
b) 3.670E+03 V·m
c) 4.037E+03 V·m
d) 4.441E+03 V·m
e) 4.885E+03 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.074E+01 N·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.989E+01 N·m2/C
b) 6.588E+01 N·m2/C
c) 7.247E+01 N·m2/C
d) 7.971E+01 N·m2/C
e) 8.769E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.457E+01 N·m2/C
b) 9.303E+01 N·m2/C
c) 1.023E+02 N·m2/C
d) 1.126E+02 N·m2/C
e) 1.238E+02 N·m2/C

#### c06 H1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{1.4}{\hat {i}}+2x^{2.3}{\hat {j}}+4y^{2.3}{\hat {k}}}$

a) 2.694E+03 V·m
b) 2.963E+03 V·m
c) 3.259E+03 V·m
d) 3.585E+03 V·m
e) 3.944E+03 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.125E+01 N·m2/C
b) 4.537E+01 N·m2/C
c) 4.991E+01 N·m2/C
d) 5.490E+01 N·m2/C
e) 6.039E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.214E+01 N·m2/C
b) 2.436E+01 N·m2/C
c) 2.679E+01 N·m2/C
d) 2.947E+01 N·m2/C
e) 3.242E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.756E+01 N·m2/C
b) 3.032E+01 N·m2/C
c) 3.335E+01 N·m2/C
d) 3.668E+01 N·m2/C
e) 4.035E+01 N·m2/C

#### c06 H2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

a) 7.200E+01 V·m
b) 7.920E+01 V·m
c) 8.712E+01 V·m
d) 9.583E+01 V·m
e) 1.054E+02 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.6 m, z=z0=1.2 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.3m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.809E+01 N·m2/C
b) 5.290E+01 N·m2/C
c) 5.819E+01 N·m2/C
d) 6.401E+01 N·m2/C
e) 7.041E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.192E+01 N·m2/C
b) 6.811E+01 N·m2/C
c) 7.492E+01 N·m2/C
d) 8.242E+01 N·m2/C
e) 9.066E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 9.823E+00 N·m2/C
b) 1.080E+01 N·m2/C
c) 1.189E+01 N·m2/C
d) 1.307E+01 N·m2/C
e) 1.438E+01 N·m2/C

### c06 I0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 5.058E+00 N/C
b) 5.564E+00 N/C
c) 6.120E+00 N/C
d) 6.732E+00 N/C
e) 7.405E+00 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

a) 9.952E+03 V·m
b) 1.095E+04 V·m
c) 1.204E+04 V·m
d) 1.325E+04 V·m
e) 1.457E+04 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.192E+01 N·m2/C
b) 6.811E+01 N·m2/C
c) 7.492E+01 N·m2/C
d) 8.242E+01 N·m2/C
e) 9.066E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.134E+01 N·m2/C
b) 2.347E+01 N·m2/C
c) 2.582E+01 N·m2/C
d) 2.840E+01 N·m2/C
e) 3.124E+01 N·m2/C

#### c06 I1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.3 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.5 m from the center of the shells?

a) 1.994E+01 N/C
b) 2.194E+01 N/C
c) 2.413E+01 N/C
d) 2.655E+01 N/C
e) 2.920E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.3}{\hat {i}}+3x^{2.4}{\hat {j}}+2y^{1.8}{\hat {k}}}$

a) 8.731E+02 V·m
b) 9.604E+02 V·m
c) 1.056E+03 V·m
d) 1.162E+03 V·m
e) 1.278E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.6 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 7.8m2. An electric field has the xyz components (0, 8.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.000E+01 N·m2/C
b) 5.500E+01 N·m2/C
c) 6.050E+01 N·m2/C
d) 6.656E+01 N·m2/C
e) 7.321E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.134E+01 N·m2/C
b) 2.347E+01 N·m2/C
c) 2.582E+01 N·m2/C
d) 2.840E+01 N·m2/C
e) 3.124E+01 N·m2/C

#### c06 I2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.777E+01 N·m2/C
b) 5.254E+01 N·m2/C
c) 5.780E+01 N·m2/C
d) 6.358E+01 N·m2/C
e) 6.993E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.730E+01 N·m2/C
b) 5.203E+01 N·m2/C
c) 5.723E+01 N·m2/C
d) 6.295E+01 N·m2/C
e) 6.925E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?

a) 5.297E+00 N/C
b) 5.827E+00 N/C
c) 6.409E+00 N/C
d) 7.050E+00 N/C
e) 7.755E+00 N/C

### c06 J0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?

a) 8.580E+00 N/C
b) 9.438E+00 N/C
c) 1.038E+01 N/C
d) 1.142E+01 N/C
e) 1.256E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

a) 1.997E+03 V·m
b) 2.197E+03 V·m
c) 2.417E+03 V·m
d) 2.659E+03 V·m
e) 2.924E+03 V·m

3) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?

a) 7.825E+02 N/C
b) 8.607E+02 N/C
c) 9.468E+02 N/C
d) 1.041E+03 N/C
e) 1.146E+03 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.891E+01 N·m2/C
b) 2.080E+01 N·m2/C
c) 2.288E+01 N·m2/C
d) 2.517E+01 N·m2/C
e) 2.768E+01 N·m2/C

#### c06 J1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

a) 8.545E+01 V·m
b) 9.400E+01 V·m
c) 1.034E+02 V·m
d) 1.137E+02 V·m
e) 1.251E+02 V·m

2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.7 (r≤R) where a=3 nC·m-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 1.390E+03 N/C
b) 1.530E+03 N/C
c) 1.682E+03 N/C
d) 1.851E+03 N/C
e) 2.036E+03 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.074E+01 N·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

a) 2.988E+00 N/C
b) 3.287E+00 N/C
c) 3.616E+00 N/C
d) 3.977E+00 N/C
e) 4.375E+00 N/C

#### c06 J2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 5.058E+00 N/C
b) 5.564E+00 N/C
c) 6.120E+00 N/C
d) 6.732E+00 N/C
e) 7.405E+00 N/C

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.079E+02 N/C
b) 2.287E+02 N/C
c) 2.516E+02 N/C
d) 2.767E+02 N/C
e) 3.044E+02 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.6 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 7.8m2. An electric field has the xyz components (0, 8.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.000E+01 N·m2/C
b) 5.500E+01 N·m2/C
c) 6.050E+01 N·m2/C
d) 6.656E+01 N·m2/C
e) 7.321E+01 N·m2/C

### c06 K0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.730E+01 N·m2/C
b) 5.203E+01 N·m2/C
c) 5.723E+01 N·m2/C
d) 6.295E+01 N·m2/C
e) 6.925E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.270E+01 N·m2/C
b) 6.897E+01 N·m2/C
c) 7.586E+01 N·m2/C
d) 8.345E+01 N·m2/C
e) 9.179E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

a) 2.067E+03 V·m
b) 2.274E+03 V·m
c) 2.501E+03 V·m
d) 2.752E+03 V·m
e) 3.027E+03 V·m

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?

a) 1.096E+00 N/C
b) 1.206E+00 N/C
c) 1.327E+00 N/C
d) 1.459E+00 N/C
e) 1.605E+00 N/C

#### c06 K1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?

a) 9.642E+00 N/C
b) 1.061E+01 N/C
c) 1.167E+01 N/C
d) 1.283E+01 N/C
e) 1.412E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.074E+01 N·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 9.823E+00 N·m2/C
b) 1.080E+01 N·m2/C
c) 1.189E+01 N·m2/C
d) 1.307E+01 N·m2/C
e) 1.438E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

a) 9.952E+03 V·m
b) 1.095E+04 V·m
c) 1.204E+04 V·m
d) 1.325E+04 V·m
e) 1.457E+04 V·m

#### c06 K2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

a) 1.128E+04 V·m
b) 1.241E+04 V·m
c) 1.365E+04 V·m
d) 1.502E+04 V·m
e) 1.652E+04 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.662E+01 N·m2/C
b) 4.028E+01 N·m2/C
c) 4.430E+01 N·m2/C
d) 4.873E+01 N·m2/C
e) 5.361E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?

a) 5.297E+00 N/C
b) 5.827E+00 N/C
c) 6.409E+00 N/C
d) 7.050E+00 N/C
e) 7.755E+00 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.074E+01 N·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C

### c06 L0

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m
b) 7.759E+03 V·m
c) 8.535E+03 V·m
d) 9.388E+03 V·m
e) 1.033E+04 V·m

2) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

a) 3.604E+02 N/C
b) 3.964E+02 N/C
c) 4.360E+02 N/C
d) 4.796E+02 N/C
e) 5.276E+02 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

a) 2.837E+01 N/C
b) 3.121E+01 N/C
c) 3.433E+01 N/C
d) 3.776E+01 N/C
e) 4.154E+01 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.777E+01 N·m2/C
b) 5.254E+01 N·m2/C
c) 5.780E+01 N·m2/C
d) 6.358E+01 N·m2/C
e) 6.993E+01 N·m2/C

#### c06 L1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m
b) 2.871E+03 V·m
c) 3.158E+03 V·m
d) 3.474E+03 V·m
e) 3.822E+03 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.012E+01 N·m2/C
b) 2.213E+01 N·m2/C
c) 2.435E+01 N·m2/C
d) 2.678E+01 N·m2/C
e) 2.946E+01 N·m2/C

3) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

a) 3.821E+02 N/C
b) 4.203E+02 N/C
c) 4.624E+02 N/C
d) 5.086E+02 N/C
e) 5.594E+02 N/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 9.144E+00 N/C
b) 1.006E+01 N/C
c) 1.106E+01 N/C
d) 1.217E+01 N/C
e) 1.339E+01 N/C

#### c06 L2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.9}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.5}{\hat {k}}}$

a) 4.286E+03 V·m
b) 4.714E+03 V·m
c) 5.186E+03 V·m
d) 5.704E+03 V·m
e) 6.275E+03 V·m

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 5.058E+00 N/C
b) 5.564E+00 N/C
c) 6.120E+00 N/C
d) 6.732E+00 N/C
e) 7.405E+00 N/C

3) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.123E+02 N/C
b) 1.235E+02 N/C
c) 1.358E+02 N/C
d) 1.494E+02 N/C
e) 1.644E+02 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.270E+01 N·m2/C
b) 6.897E+01 N·m2/C
c) 7.586E+01 N·m2/C
d) 8.345E+01 N·m2/C
e) 9.179E+01 N·m2/C

### c06 M0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.385E+01 N·m2/C
b) 5.923E+01 N·m2/C
c) 6.516E+01 N·m2/C
d) 7.167E+01 N·m2/C
e) 7.884E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.750E+01 N·m2/C
b) 4.125E+01 N·m2/C
c) 4.537E+01 N·m2/C
d) 4.991E+01 N·m2/C
e) 5.490E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.740E+01 N·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.5 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

a) 2.601E+01 N/C
b) 2.861E+01 N/C
c) 3.147E+01 N/C
d) 3.462E+01 N/C
e) 3.808E+01 N/C

#### c06 M1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.6 m, z=z0=1.4 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.959E+01 N·m2/C
b) 4.354E+01 N·m2/C
c) 4.790E+01 N·m2/C
d) 5.269E+01 N·m2/C
e) 5.796E+01 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

a) 3.251E+01 N/C
b) 3.577E+01 N/C
c) 3.934E+01 N/C
d) 4.328E+01 N/C
e) 4.760E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.698E+01 N·m2/C
b) 1.868E+01 N·m2/C
c) 2.055E+01 N·m2/C
d) 2.260E+01 N·m2/C
e) 2.486E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.614E+01 N·m2/C
b) 7.275E+01 N·m2/C
c) 8.003E+01 N·m2/C
d) 8.803E+01 N·m2/C
e) 9.683E+01 N·m2/C

#### c06 M2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

a) 3.251E+01 N/C
b) 3.577E+01 N/C
c) 3.934E+01 N/C
d) 4.328E+01 N/C
e) 4.760E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.901E+01 N·m2/C
b) 3.192E+01 N·m2/C
c) 3.511E+01 N·m2/C
d) 3.862E+01 N·m2/C
e) 4.248E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.9 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 6.8m2 ,and those in the zx plane have area 7.7m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.898E+01 N·m2/C
b) 7.588E+01 N·m2/C
c) 8.347E+01 N·m2/C
d) 9.181E+01 N·m2/C
e) 1.010E+02 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.989E+01 N·m2/C
b) 6.588E+01 N·m2/C
c) 7.247E+01 N·m2/C
d) 7.971E+01 N·m2/C
e) 8.769E+01 N·m2/C

### c06 N0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

a) 1.491E+01 N/C
b) 1.640E+01 N/C
c) 1.804E+01 N/C
d) 1.984E+01 N/C
e) 2.182E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.6 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 7.8m2. An electric field has the xyz components (0, 8.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.000E+01 N·m2/C
b) 5.500E+01 N·m2/C
c) 6.050E+01 N·m2/C
d) 6.656E+01 N·m2/C
e) 7.321E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.756E+01 N·m2/C
b) 3.032E+01 N·m2/C
c) 3.335E+01 N·m2/C
d) 3.668E+01 N·m2/C
e) 4.035E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}}$

a) 1.206E+03 V·m
b) 1.326E+03 V·m
c) 1.459E+03 V·m
d) 1.605E+03 V·m
e) 1.765E+03 V·m

#### c06 N1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.3 m, z=z0=1.3 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 5.7m2. An electric field has the xyz components (0, 5.7, 7.5) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.249E+01 N·m2/C
b) 3.574E+01 N·m2/C
c) 3.931E+01 N·m2/C
d) 4.324E+01 N·m2/C
e) 4.757E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

a) 2.067E+03 V·m
b) 2.274E+03 V·m
c) 2.501E+03 V·m
d) 2.752E+03 V·m
e) 3.027E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.012E+01 N·m2/C
b) 2.213E+01 N·m2/C
c) 2.435E+01 N·m2/C
d) 2.678E+01 N·m2/C
e) 2.946E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?

a) 9.592E+00 N/C
b) 1.055E+01 N/C
c) 1.161E+01 N/C
d) 1.277E+01 N/C
e) 1.404E+01 N/C

#### c06 N2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.756E+01 N·m2/C
b) 3.032E+01 N·m2/C
c) 3.335E+01 N·m2/C
d) 3.668E+01 N·m2/C
e) 4.035E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.740E+01 N·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?

a) 1.096E+00 N/C
b) 1.206E+00 N/C
c) 1.327E+00 N/C
d) 1.459E+00 N/C
e) 1.605E+00 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m
b) 7.759E+03 V·m
c) 8.535E+03 V·m
d) 9.388E+03 V·m
e) 1.033E+04 V·m

### c06 O0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.891E+01 N·m2/C
b) 2.080E+01 N·m2/C
c) 2.288E+01 N·m2/C
d) 2.517E+01 N·m2/C
e) 2.768E+01 N·m2/C

2) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.579E+02 N/C
b) 2.837E+02 N/C
c) 3.121E+02 N/C
d) 3.433E+02 N/C
e) 3.776E+02 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

a) 9.952E+03 V·m
b) 1.095E+04 V·m
c) 1.204E+04 V·m
d) 1.325E+04 V·m
e) 1.457E+04 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.5 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 8.3m2. Those in the xy plane have area 5.7m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.408E+01 N·m2/C
b) 5.949E+01 N·m2/C
c) 6.544E+01 N·m2/C
d) 7.198E+01 N·m2/C
e) 7.918E+01 N·m2/C

#### c06 O1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.6 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 7.8m2. An electric field has the xyz components (0, 8.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.000E+01 N·m2/C
b) 5.500E+01 N·m2/C
c) 6.050E+01 N·m2/C
d) 6.656E+01 N·m2/C
e) 7.321E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.737E+01 N·m2/C
b) 1.910E+01 N·m2/C
c) 2.101E+01 N·m2/C
d) 2.311E+01 N·m2/C
e) 2.543E+01 N·m2/C

3) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 6.411E+02 N/C
b) 7.052E+02 N/C
c) 7.757E+02 N/C
d) 8.533E+02 N/C
e) 9.386E+02 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

a) 3.337E+03 V·m
b) 3.670E+03 V·m
c) 4.037E+03 V·m
d) 4.441E+03 V·m
e) 4.885E+03 V·m

#### c06 O2

1) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?

a) 2.777E+02 N/C
b) 3.055E+02 N/C
c) 3.361E+02 N/C
d) 3.697E+02 N/C
e) 4.066E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

a) 7.200E+01 V·m
b) 7.920E+01 V·m
c) 8.712E+01 V·m
d) 9.583E+01 V·m
e) 1.054E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.0 m, z=z0=1.9 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.9m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 2.9m2. An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.388E+01 N·m2/C
b) 1.526E+01 N·m2/C
c) 1.679E+01 N·m2/C
d) 1.847E+01 N·m2/C
e) 2.032E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.6m2 ,and those in the zx plane have area 13.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 46° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.988E+01 N·m2/C
b) 5.487E+01 N·m2/C
c) 6.035E+01 N·m2/C
d) 6.639E+01 N·m2/C
e) 7.303E+01 N·m2/C

### c06 P0

1) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

a) 1.383E+02 N/C
b) 1.522E+02 N/C
c) 1.674E+02 N/C
d) 1.841E+02 N/C
e) 2.025E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

a) 2.210E+04 V·m
b) 2.431E+04 V·m
c) 2.674E+04 V·m
d) 2.941E+04 V·m
e) 3.235E+04 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.695E+01 N·m2/C
b) 4.065E+01 N·m2/C
c) 4.472E+01 N·m2/C
d) 4.919E+01 N·m2/C
e) 5.411E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.6 m, z=z0=1.4 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.959E+01 N·m2/C
b) 4.354E+01 N·m2/C
c) 4.790E+01 N·m2/C
d) 5.269E+01 N·m2/C
e) 5.796E+01 N·m2/C

#### c06 P1

1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.7 (r≤R) where a=3 nC·m-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 1.390E+03 N/C
b) 1.530E+03 N/C
c) 1.682E+03 N/C
d) 1.851E+03 N/C
e) 2.036E+03 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.737E+01 N·m2/C
b) 1.910E+01 N·m2/C
c) 2.101E+01 N·m2/C
d) 2.311E+01 N·m2/C
e) 2.543E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.876E+01 N·m2/C
b) 8.664E+01 N·m2/C
c) 9.531E+01 N·m2/C
d) 1.048E+02 N·m2/C
e) 1.153E+02 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

a) 9.952E+03 V·m
b) 1.095E+04 V·m
c) 1.204E+04 V·m
d) 1.325E+04 V·m
e) 1.457E+04 V·m

#### c06 P2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.012E+01 N·m2/C
b) 2.213E+01 N·m2/C
c) 2.435E+01 N·m2/C
d) 2.678E+01 N·m2/C
e) 2.946E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.698E+01 N·m2/C
b) 1.868E+01 N·m2/C
c) 2.055E+01 N·m2/C
d) 2.260E+01 N·m2/C
e) 2.486E+01 N·m2/C

3) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

a) 3.604E+02 N/C
b) 3.964E+02 N/C
c) 4.360E+02 N/C
d) 4.796E+02 N/C
e) 5.276E+02 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

a) 3.429E+03 V·m
b) 3.771E+03 V·m
c) 4.149E+03 V·m
d) 4.564E+03 V·m
e) 5.020E+03 V·m

### c06 Q0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.270E+01 N·m2/C
b) 6.897E+01 N·m2/C
c) 7.586E+01 N·m2/C
d) 8.345E+01 N·m2/C
e) 9.179E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.730E+01 N·m2/C
b) 5.203E+01 N·m2/C
c) 5.723E+01 N·m2/C
d) 6.295E+01 N·m2/C
e) 6.925E+01 N·m2/C

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.579E+02 N/C
b) 2.837E+02 N/C
c) 3.121E+02 N/C
d) 3.433E+02 N/C
e) 3.776E+02 N/C

#### c06 Q1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m
b) 2.871E+03 V·m
c) 3.158E+03 V·m
d) 3.474E+03 V·m
e) 3.822E+03 V·m

2) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?

a) 2.285E+01 N/C
b) 2.514E+01 N/C
c) 2.765E+01 N/C
d) 3.042E+01 N/C
e) 3.346E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.891E+01 N·m2/C
b) 2.080E+01 N·m2/C
c) 2.288E+01 N·m2/C
d) 2.517E+01 N·m2/C
e) 2.768E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.6m2 ,and those in the zx plane have area 13.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 46° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.988E+01 N·m2/C
b) 5.487E+01 N·m2/C
c) 6.035E+01 N·m2/C
d) 6.639E+01 N·m2/C
e) 7.303E+01 N·m2/C

#### c06 Q2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.777E+01 N·m2/C
b) 5.254E+01 N·m2/C
c) 5.780E+01 N·m2/C
d) 6.358E+01 N·m2/C
e) 6.993E+01 N·m2/C

2) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?

a) 4.782E+02 N/C
b) 5.260E+02 N/C
c) 5.787E+02 N/C
d) 6.365E+02 N/C
e) 7.002E+02 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.125E+01 N·m2/C
b) 4.537E+01 N·m2/C
c) 4.991E+01 N·m2/C
d) 5.490E+01 N·m2/C
e) 6.039E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

a) 7.200E+01 V·m
b) 7.920E+01 V·m
c) 8.712E+01 V·m
d) 9.583E+01 V·m
e) 1.054E+02 V·m

### c06 R0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.5 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 8.3m2. Those in the xy plane have area 5.7m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.408E+01 N·m2/C
b) 5.949E+01 N·m2/C
c) 6.544E+01 N·m2/C
d) 7.198E+01 N·m2/C
e) 7.918E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.3}{\hat {i}}+3x^{2.4}{\hat {j}}+2y^{1.8}{\hat {k}}}$

a) 8.731E+02 V·m
b) 9.604E+02 V·m
c) 1.056E+03 V·m
d) 1.162E+03 V·m
e) 1.278E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.3 m, z=z0=1.3 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 5.7m2. An electric field has the xyz components (0, 5.7, 7.5) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.249E+01 N·m2/C
b) 3.574E+01 N·m2/C
c) 3.931E+01 N·m2/C
d) 4.324E+01 N·m2/C
e) 4.757E+01 N·m2/C

4) A non-conducting sphere of radius R=1.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.6 (r≤R) where a=2 nC·m-1.4. What is the magnitude of the electric field at a distance of 0.76 m from the center?

a) 2.406E+01 N/C
b) 2.646E+01 N/C
c) 2.911E+01 N/C
d) 3.202E+01 N/C
e) 3.522E+01 N/C

#### c06 R1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.740E+01 N·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.439E+01 N·m2/C
b) 5.983E+01 N·m2/C
c) 6.581E+01 N·m2/C
d) 7.239E+01 N·m2/C
e) 7.963E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m

4) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 6.411E+02 N/C
b) 7.052E+02 N/C
c) 7.757E+02 N/C
d) 8.533E+02 N/C
e) 9.386E+02 N/C

#### c06 R2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.079E+02 N/C
b) 2.287E+02 N/C
c) 2.516E+02 N/C
d) 2.767E+02 N/C
e) 3.044E+02 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.314E+01 N·m2/C
b) 9.146E+01 N·m2/C
c) 1.006E+02 N·m2/C
d) 1.107E+02 N·m2/C
e) 1.217E+02 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.901E+01 N·m2/C
b) 3.192E+01 N·m2/C
c) 3.511E+01 N·m2/C
d) 3.862E+01 N·m2/C
e) 4.248E+01 N·m2/C

### c06 S0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.992E+01 N·m2/C
b) 2.192E+01 N·m2/C
c) 2.411E+01 N·m2/C
d) 2.652E+01 N·m2/C
e) 2.917E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.891E+01 N·m2/C
b) 2.080E+01 N·m2/C
c) 2.288E+01 N·m2/C
d) 2.517E+01 N·m2/C
e) 2.768E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

a) 3.337E+03 V·m
b) 3.670E+03 V·m
c) 4.037E+03 V·m
d) 4.441E+03 V·m
e) 4.885E+03 V·m

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?

a) 8.580E+00 N/C
b) 9.438E+00 N/C
c) 1.038E+01 N/C
d) 1.142E+01 N/C
e) 1.256E+01 N/C

#### c06 S1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

a) 2.210E+04 V·m
b) 2.431E+04 V·m
c) 2.674E+04 V·m
d) 2.941E+04 V·m
e) 3.235E+04 V·m

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

a) 2.964E+00 N/C
b) 3.260E+00 N/C
c) 3.586E+00 N/C
d) 3.944E+00 N/C
e) 4.339E+00 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.730E+01 N·m2/C
b) 5.203E+01 N·m2/C
c) 5.723E+01 N·m2/C
d) 6.295E+01 N·m2/C
e) 6.925E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.876E+01 N·m2/C
b) 8.664E+01 N·m2/C
c) 9.531E+01 N·m2/C
d) 1.048E+02 N·m2/C
e) 1.153E+02 N·m2/C

#### c06 S2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

a) 1.114E+01 N/C
b) 1.225E+01 N/C
c) 1.347E+01 N/C
d) 1.482E+01 N/C
e) 1.630E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.920E+01 N·m2/C
b) 7.612E+01 N·m2/C
c) 8.373E+01 N·m2/C
d) 9.210E+01 N·m2/C
e) 1.013E+02 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.125E+01 N·m2/C
b) 4.537E+01 N·m2/C
c) 4.991E+01 N·m2/C
d) 5.490E+01 N·m2/C
e) 6.039E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.0}{\hat {i}}+2x^{2.1}{\hat {j}}+3y^{2.5}{\hat {k}}}$

a) 9.027E+03 V·m
b) 9.930E+03 V·m
c) 1.092E+04 V·m
d) 1.202E+04 V·m
e) 1.322E+04 V·m

### c06 T0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.695E+01 N·m2/C
b) 4.065E+01 N·m2/C
c) 4.472E+01 N·m2/C
d) 4.919E+01 N·m2/C
e) 5.411E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.756E+01 N·m2/C
b) 3.032E+01 N·m2/C
c) 3.335E+01 N·m2/C
d) 3.668E+01 N·m2/C
e) 4.035E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.891E+01 N·m2/C
b) 2.080E+01 N·m2/C
c) 2.288E+01 N·m2/C
d) 2.517E+01 N·m2/C
e) 2.768E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.0}{\hat {i}}+2x^{2.1}{\hat {j}}+3y^{2.5}{\hat {k}}}$

a) 9.027E+03 V·m
b) 9.930E+03 V·m
c) 1.092E+04 V·m
d) 1.202E+04 V·m
e) 1.322E+04 V·m

#### c06 T1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.712E+01 N·m2/C
b) 4.083E+01 N·m2/C
c) 4.491E+01 N·m2/C
d) 4.940E+01 N·m2/C
e) 5.434E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.134E+01 N·m2/C
b) 2.347E+01 N·m2/C
c) 2.582E+01 N·m2/C
d) 2.840E+01 N·m2/C
e) 3.124E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.2 m, z=z0=1.9 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 8.1m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 8.5, 6.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 7.081E+01 N·m2/C
b) 7.789E+01 N·m2/C
c) 8.568E+01 N·m2/C
d) 9.425E+01 N·m2/C
e) 1.037E+02 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m

#### c06 T2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

a) 7.054E+03 V·m
b) 7.759E+03 V·m
c) 8.535E+03 V·m
d) 9.388E+03 V·m
e) 1.033E+04 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.921E+01 N·m2/C
b) 9.813E+01 N·m2/C
c) 1.079E+02 N·m2/C
d) 1.187E+02 N·m2/C
e) 1.306E+02 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.8 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 3.9m2 ,and those in the zx plane have area 4.3m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 31° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.521E+01 N·m2/C
b) 4.973E+01 N·m2/C
c) 5.470E+01 N·m2/C
d) 6.017E+01 N·m2/C
e) 6.619E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.2 m, and z=z1=4.1 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 5.8m2. An electric field has the xyz components (0, 8.4, 5.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.328E+01 N·m2/C
b) 3.660E+01 N·m2/C
c) 4.026E+01 N·m2/C
d) 4.429E+01 N·m2/C
e) 4.872E+01 N·m2/C

### c06 U0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.921E+01 N·m2/C
b) 9.813E+01 N·m2/C
c) 1.079E+02 N·m2/C
d) 1.187E+02 N·m2/C
e) 1.306E+02 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.8 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 3.9m2 ,and those in the zx plane have area 4.3m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 31° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.521E+01 N·m2/C
b) 4.973E+01 N·m2/C
c) 5.470E+01 N·m2/C
d) 6.017E+01 N·m2/C
e) 6.619E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

a) 1.491E+01 N/C
b) 1.640E+01 N/C
c) 1.804E+01 N/C
d) 1.984E+01 N/C
e) 2.182E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

a) 3.429E+03 V·m
b) 3.771E+03 V·m
c) 4.149E+03 V·m
d) 4.564E+03 V·m
e) 5.020E+03 V·m

#### c06 U1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.012E+01 N·m2/C
b) 2.213E+01 N·m2/C
c) 2.435E+01 N·m2/C
d) 2.678E+01 N·m2/C
e) 2.946E+01 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

a) 2.964E+00 N/C
b) 3.260E+00 N/C
c) 3.586E+00 N/C
d) 3.944E+00 N/C
e) 4.339E+00 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

a) 7.200E+01 V·m
b) 7.920E+01 V·m
c) 8.712E+01 V·m
d) 9.583E+01 V·m
e) 1.054E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.457E+01 N·m2/C
b) 9.303E+01 N·m2/C
c) 1.023E+02 N·m2/C
d) 1.126E+02 N·m2/C
e) 1.238E+02 N·m2/C

#### c06 U2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.415E+01 N·m2/C
b) 9.256E+01 N·m2/C
c) 1.018E+02 N·m2/C
d) 1.120E+02 N·m2/C
e) 1.232E+02 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

a) 1.491E+01 N/C
b) 1.640E+01 N/C
c) 1.804E+01 N/C
d) 1.984E+01 N/C
e) 2.182E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.8 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 3.9m2 ,and those in the zx plane have area 4.3m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 31° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.521E+01 N·m2/C
b) 4.973E+01 N·m2/C
c) 5.470E+01 N·m2/C
d) 6.017E+01 N·m2/C
e) 6.619E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

a) 9.952E+03 V·m
b) 1.095E+04 V·m
c) 1.204E+04 V·m
d) 1.325E+04 V·m
e) 1.457E+04 V·m

### c06 V0

1) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

a) 3.604E+02 N/C
b) 3.964E+02 N/C
c) 4.360E+02 N/C
d) 4.796E+02 N/C
e) 5.276E+02 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 5.058E+00 N/C
b) 5.564E+00 N/C
c) 6.120E+00 N/C
d) 6.732E+00 N/C
e) 7.405E+00 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.415E+01 N·m2/C
b) 9.256E+01 N·m2/C
c) 1.018E+02 N·m2/C
d) 1.120E+02 N·m2/C
e) 1.232E+02 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.992E+01 N·m2/C
b) 2.192E+01 N·m2/C
c) 2.411E+01 N·m2/C
d) 2.652E+01 N·m2/C
e) 2.917E+01 N·m2/C

#### c06 V1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.214E+01 N·m2/C
b) 2.436E+01 N·m2/C
c) 2.679E+01 N·m2/C
d) 2.947E+01 N·m2/C
e) 3.242E+01 N·m2/C

2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.012E+01 N·m2/C
b) 2.213E+01 N·m2/C
c) 2.435E+01 N·m2/C
d) 2.678E+01 N·m2/C
e) 2.946E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

a) 5.058E+00 N/C
b) 5.564E+00 N/C
c) 6.120E+00 N/C
d) 6.732E+00 N/C
e) 7.405E+00 N/C

#### c06 V2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.186E+01 N·m2/C
b) 2.404E+01 N·m2/C
c) 2.645E+01 N·m2/C
d) 2.909E+01 N·m2/C
e) 3.200E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 9.823E+00 N·m2/C
b) 1.080E+01 N·m2/C
c) 1.189E+01 N·m2/C
d) 1.307E+01 N·m2/C
e) 1.438E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

a) 2.964E+00 N/C
b) 3.260E+00 N/C
c) 3.586E+00 N/C
d) 3.944E+00 N/C
e) 4.339E+00 N/C

4) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

a) 3.797E+01 N/C
b) 4.177E+01 N/C
c) 4.595E+01 N/C
d) 5.054E+01 N/C
e) 5.560E+01 N/C

### c06 W0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.214E+01 N·m2/C
b) 2.436E+01 N·m2/C
c) 2.679E+01 N·m2/C
d) 2.947E+01 N·m2/C
e) 3.242E+01 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

a) 1.114E+01 N/C
b) 1.225E+01 N/C
c) 1.347E+01 N/C
d) 1.482E+01 N/C
e) 1.630E+01 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.439E+01 N·m2/C
b) 5.983E+01 N·m2/C
c) 6.581E+01 N·m2/C
d) 7.239E+01 N·m2/C
e) 7.963E+01 N·m2/C

#### c06 W1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.314E+01 N·m2/C
b) 9.146E+01 N·m2/C
c) 1.006E+02 N·m2/C
d) 1.107E+02 N·m2/C
e) 1.217E+02 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?

a) 9.592E+00 N/C
b) 1.055E+01 N/C
c) 1.161E+01 N/C
d) 1.277E+01 N/C
e) 1.404E+01 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

a) 1.128E+04 V·m
b) 1.241E+04 V·m
c) 1.365E+04 V·m
d) 1.502E+04 V·m
e) 1.652E+04 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 2.214E+01 N·m2/C
b) 2.436E+01 N·m2/C
c) 2.679E+01 N·m2/C
d) 2.947E+01 N·m2/C
e) 3.242E+01 N·m2/C

#### c06 W2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.750E+01 N·m2/C
b) 4.125E+01 N·m2/C
c) 4.537E+01 N·m2/C
d) 4.991E+01 N·m2/C
e) 5.490E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}}$

a) 1.206E+03 V·m
b) 1.326E+03 V·m
c) 1.459E+03 V·m
d) 1.605E+03 V·m
e) 1.765E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.698E+01 N·m2/C
b) 1.868E+01 N·m2/C
c) 2.055E+01 N·m2/C
d) 2.260E+01 N·m2/C
e) 2.486E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

a) 3.251E+01 N/C
b) 3.577E+01 N/C
c) 3.934E+01 N/C
d) 4.328E+01 N/C
e) 4.760E+01 N/C

### c06 X0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.9 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 8.1m2. An electric field has the xyz components (0, 8.1, 6.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.529E+01 N·m2/C
b) 7.181E+01 N·m2/C
c) 7.900E+01 N·m2/C
d) 8.690E+01 N·m2/C
e) 9.559E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

a) 1.969E+02 V·m
b) 2.166E+02 V·m
c) 2.383E+02 V·m
d) 2.621E+02 V·m
e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.439E+01 N·m2/C
b) 5.983E+01 N·m2/C
c) 6.581E+01 N·m2/C
d) 7.239E+01 N·m2/C
e) 7.963E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

a) 2.988E+00 N/C
b) 3.287E+00 N/C
c) 3.616E+00 N/C
d) 3.977E+00 N/C
e) 4.375E+00 N/C

#### c06 X1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

a) 2.610E+03 V·m
b) 2.871E+03 V·m
c) 3.158E+03 V·m
d) 3.474E+03 V·m
e) 3.822E+03 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.4 m, z=z0=1.5 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 4.6m2 ,and those in the zx plane have area 6.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.222E+01 N·m2/C
b) 3.544E+01 N·m2/C
c) 3.899E+01 N·m2/C
d) 4.289E+01 N·m2/C
e) 4.718E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

a) 1.114E+01 N/C
b) 1.225E+01 N/C
c) 1.347E+01 N/C
d) 1.482E+01 N/C
e) 1.630E+01 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.614E+01 N·m2/C
b) 7.275E+01 N·m2/C
c) 8.003E+01 N·m2/C
d) 8.803E+01 N·m2/C
e) 9.683E+01 N·m2/C

#### c06 X2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

a) 2.988E+00 N/C
b) 3.287E+00 N/C
c) 3.616E+00 N/C
d) 3.977E+00 N/C
e) 4.375E+00 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

a) 3.429E+03 V·m
b) 3.771E+03 V·m
c) 4.149E+03 V·m
d) 4.564E+03 V·m
e) 5.020E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.074E+01 N·m2/C
b) 3.382E+01 N·m2/C
c) 3.720E+01 N·m2/C
d) 4.092E+01 N·m2/C
e) 4.501E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.270E+01 N·m2/C
b) 6.897E+01 N·m2/C
c) 7.586E+01 N·m2/C
d) 8.345E+01 N·m2/C
e) 9.179E+01 N·m2/C

### c06 Y0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.314E+01 N·m2/C
b) 9.146E+01 N·m2/C
c) 1.006E+02 N·m2/C
d) 1.107E+02 N·m2/C
e) 1.217E+02 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

a) 1.114E+01 N/C
b) 1.225E+01 N/C
c) 1.347E+01 N/C
d) 1.482E+01 N/C
e) 1.630E+01 N/C

3) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

a) 2.274E+02 N/C
b) 2.501E+02 N/C
c) 2.751E+02 N/C
d) 3.026E+02 N/C
e) 3.329E+02 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.3}{\hat {i}}+3x^{2.4}{\hat {j}}+2y^{1.8}{\hat {k}}}$

a) 8.731E+02 V·m
b) 9.604E+02 V·m
c) 1.056E+03 V·m
d) 1.162E+03 V·m
e) 1.278E+03 V·m

#### c06 Y1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?

a) 8.580E+00 N/C
b) 9.438E+00 N/C
c) 1.038E+01 N/C
d) 1.142E+01 N/C
e) 1.256E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.989E+01 N·m2/C
b) 6.588E+01 N·m2/C
c) 7.247E+01 N·m2/C
d) 7.971E+01 N·m2/C
e) 8.769E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

a) 8.545E+01 V·m
b) 9.400E+01 V·m
c) 1.034E+02 V·m
d) 1.137E+02 V·m
e) 1.251E+02 V·m

4) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.079E+02 N/C
b) 2.287E+02 N/C
c) 2.516E+02 N/C
d) 2.767E+02 N/C
e) 3.044E+02 N/C

#### c06 Y2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

a) 2.837E+01 N/C
b) 3.121E+01 N/C
c) 3.433E+01 N/C
d) 3.776E+01 N/C
e) 4.154E+01 N/C

2) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 6.411E+02 N/C
b) 7.052E+02 N/C
c) 7.757E+02 N/C
d) 8.533E+02 N/C
e) 9.386E+02 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.4 m, z=z0=1.5 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 4.6m2 ,and those in the zx plane have area 6.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.222E+01 N·m2/C
b) 3.544E+01 N·m2/C
c) 3.899E+01 N·m2/C
d) 4.289E+01 N·m2/C
e) 4.718E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

a) 1.128E+04 V·m
b) 1.241E+04 V·m
c) 1.365E+04 V·m
d) 1.502E+04 V·m
e) 1.652E+04 V·m

### c06 Z0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 8.415E+01 N·m2/C
b) 9.256E+01 N·m2/C
c) 1.018E+02 N·m2/C
d) 1.120E+02 N·m2/C
e) 1.232E+02 N·m2/C

2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.7 (r≤R) where a=3 nC·m-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

a) 1.390E+03 N/C
b) 1.530E+03 N/C
c) 1.682E+03 N/C
d) 1.851E+03 N/C
e) 2.036E+03 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.920E+01 N·m2/C
b) 7.612E+01 N·m2/C
c) 8.373E+01 N·m2/C
d) 9.210E+01 N·m2/C
e) 1.013E+02 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 4.125E+01 N·m2/C
b) 4.537E+01 N·m2/C
c) 4.991E+01 N·m2/C
d) 5.490E+01 N·m2/C
e) 6.039E+01 N·m2/C

#### c06 Z1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.920E+01 N·m2/C
b) 7.612E+01 N·m2/C
c) 8.373E+01 N·m2/C
d) 9.210E+01 N·m2/C
e) 1.013E+02 N·m2/C

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

a) 2.079E+02 N/C
b) 2.287E+02 N/C
c) 2.516E+02 N/C
d) 2.767E+02 N/C
e) 3.044E+02 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 6.614E+01 N·m2/C
b) 7.275E+01 N·m2/C
c) 8.003E+01 N·m2/C
d) 8.803E+01 N·m2/C
e) 9.683E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 5.439E+01 N·m2/C
b) 5.983E+01 N·m2/C
c) 6.581E+01 N·m2/C
d) 7.239E+01 N·m2/C
e) 7.963E+01 N·m2/C

#### c06 Z2

1) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

a) 3.821E+02 N/C
b) 4.203E+02 N/C
c) 4.624E+02 N/C
d) 5.086E+02 N/C
e) 5.594E+02 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.712E+01 N·m2/C
b) 4.083E+01 N·m2/C
c) 4.491E+01 N·m2/C
d) 4.940E+01 N·m2/C
e) 5.434E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 3.750E+01 N·m2/C
b) 4.125E+01 N·m2/C
c) 4.537E+01 N·m2/C
d) 4.991E+01 N·m2/C
e) 5.490E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
a) 1.740E+01 N·m2/C
b) 1.914E+01 N·m2/C
c) 2.106E+01 N·m2/C
d) 2.316E+01 N·m2/C
e) 2.548E+01 N·m2/C

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### Key: A0

1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?

+a) 7.825E+02 N/C
-b) 8.607E+02 N/C
-c) 9.468E+02 N/C
-d) 1.041E+03 N/C
-e) 1.146E+03 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

-a) 2.964E+00 N/C
-b) 3.260E+00 N/C
-c) 3.586E+00 N/C
+d) 3.944E+00 N/C
-e) 4.339E+00 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.1 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.606E+01 N·m2/C
-b) 6.167E+01 N·m2/C
-c) 6.784E+01 N·m2/C
+d) 7.462E+01 N·m2/C
-e) 8.208E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

-a) 2.067E+03 V·m
-b) 2.274E+03 V·m
+c) 2.501E+03 V·m
-d) 2.752E+03 V·m
-e) 3.027E+03 V·m

Click these links for the keys:

#### Key: A1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.6 m, z=z0=1.2 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.3m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.809E+01 N·m2/C
-b) 5.290E+01 N·m2/C
+c) 5.819E+01 N·m2/C
-d) 6.401E+01 N·m2/C
-e) 7.041E+01 N·m2/C

2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?

-a) 2.039E+01 N/C
-b) 2.243E+01 N/C
+c) 2.467E+01 N/C
-d) 2.714E+01 N/C
-e) 2.985E+01 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

-a) 9.144E+00 N/C
-b) 1.006E+01 N/C
-c) 1.106E+01 N/C
-d) 1.217E+01 N/C
+e) 1.339E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

-a) 2.610E+03 V·m
-b) 2.871E+03 V·m
+c) 3.158E+03 V·m
-d) 3.474E+03 V·m
-e) 3.822E+03 V·m

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#### Key: A2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 7.876E+01 N·m2/C
-b) 8.664E+01 N·m2/C
-c) 9.531E+01 N·m2/C
-d) 1.048E+02 N·m2/C
-e) 1.153E+02 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

-a) 2.067E+03 V·m
-b) 2.274E+03 V·m
+c) 2.501E+03 V·m
-d) 2.752E+03 V·m
-e) 3.027E+03 V·m

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?

-a) 5.297E+00 N/C
-b) 5.827E+00 N/C
-c) 6.409E+00 N/C
-d) 7.050E+00 N/C
+e) 7.755E+00 N/C

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

+a) 1.383E+02 N/C
-b) 1.522E+02 N/C
-c) 1.674E+02 N/C
-d) 1.841E+02 N/C
-e) 2.025E+02 N/C

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### Key: B0

1) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

-a) 1.123E+02 N/C
-b) 1.235E+02 N/C
+c) 1.358E+02 N/C
-d) 1.494E+02 N/C
-e) 1.644E+02 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 5.3m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 7.793E+01 N·m2/C
-b) 8.572E+01 N·m2/C
-c) 9.429E+01 N·m2/C
-d) 1.037E+02 N·m2/C
-e) 1.141E+02 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

+a) 7.200E+01 V·m
-b) 7.920E+01 V·m
-c) 8.712E+01 V·m
-d) 9.583E+01 V·m
-e) 1.054E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 6.192E+01 N·m2/C
-b) 6.811E+01 N·m2/C
-c) 7.492E+01 N·m2/C
-d) 8.242E+01 N·m2/C
-e) 9.066E+01 N·m2/C

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#### Key: B1

1) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

+a) 1.383E+02 N/C
-b) 1.522E+02 N/C
-c) 1.674E+02 N/C
-d) 1.841E+02 N/C
-e) 2.025E+02 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 5.978E+01 N·m2/C
-b) 6.576E+01 N·m2/C
-c) 7.233E+01 N·m2/C
-d) 7.957E+01 N·m2/C
-e) 8.752E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

-a) 1.997E+03 V·m
+b) 2.197E+03 V·m
-c) 2.417E+03 V·m
-d) 2.659E+03 V·m
-e) 2.924E+03 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.1 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 60° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.606E+01 N·m2/C
-b) 6.167E+01 N·m2/C
-c) 6.784E+01 N·m2/C
+d) 7.462E+01 N·m2/C
-e) 8.208E+01 N·m2/C

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#### Key: B2

1) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

+a) 3.604E+02 N/C
-b) 3.964E+02 N/C
-c) 4.360E+02 N/C
-d) 4.796E+02 N/C
-e) 5.276E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 5.978E+01 N·m2/C
-b) 6.576E+01 N·m2/C
-c) 7.233E+01 N·m2/C
-d) 7.957E+01 N·m2/C
-e) 8.752E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.214E+01 N·m2/C
-b) 2.436E+01 N·m2/C
-c) 2.679E+01 N·m2/C
-d) 2.947E+01 N·m2/C
+e) 3.242E+01 N·m2/C

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### Key: C0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 16 N/C has components in the y and z directions and is directed at 53° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.420E+01 N·m2/C
-b) 4.862E+01 N·m2/C
-c) 5.348E+01 N·m2/C
-d) 5.882E+01 N·m2/C
+e) 6.471E+01 N·m2/C

2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.64 m from the center?

-a) 2.039E+01 N/C
-b) 2.243E+01 N/C
+c) 2.467E+01 N/C
-d) 2.714E+01 N/C
-e) 2.985E+01 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

-a) 2.988E+00 N/C
-b) 3.287E+00 N/C
-c) 3.616E+00 N/C
-d) 3.977E+00 N/C
+e) 4.375E+00 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 9.823E+00 N·m2/C
+b) 1.080E+01 N·m2/C
-c) 1.189E+01 N·m2/C
-d) 1.307E+01 N·m2/C
-e) 1.438E+01 N·m2/C

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#### Key: C1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?

-a) 9.642E+00 N/C
-b) 1.061E+01 N/C
+c) 1.167E+01 N/C
-d) 1.283E+01 N/C
-e) 1.412E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 8.415E+01 N·m2/C
-b) 9.256E+01 N·m2/C
-c) 1.018E+02 N·m2/C
+d) 1.120E+02 N·m2/C
-e) 1.232E+02 N·m2/C

3) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

+a) 3.797E+01 N/C
-b) 4.177E+01 N/C
-c) 4.595E+01 N/C
-d) 5.054E+01 N/C
-e) 5.560E+01 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.214E+01 N·m2/C
-b) 2.436E+01 N·m2/C
-c) 2.679E+01 N·m2/C
-d) 2.947E+01 N·m2/C
+e) 3.242E+01 N·m2/C

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#### Key: C2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.662E+01 N·m2/C
+b) 4.028E+01 N·m2/C
-c) 4.430E+01 N·m2/C
-d) 4.873E+01 N·m2/C
-e) 5.361E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.992E+01 N·m2/C
-b) 2.192E+01 N·m2/C
+c) 2.411E+01 N·m2/C
-d) 2.652E+01 N·m2/C
-e) 2.917E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

-a) 9.144E+00 N/C
-b) 1.006E+01 N/C
-c) 1.106E+01 N/C
-d) 1.217E+01 N/C
+e) 1.339E+01 N/C

4) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?

+a) 7.825E+02 N/C
-b) 8.607E+02 N/C
-c) 9.468E+02 N/C
-d) 1.041E+03 N/C
-e) 1.146E+03 N/C

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### Key: D0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.5 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 8.3m2. Those in the xy plane have area 5.7m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.408E+01 N·m2/C
+b) 5.949E+01 N·m2/C
-c) 6.544E+01 N·m2/C
-d) 7.198E+01 N·m2/C
-e) 7.918E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

-a) 1.128E+04 V·m
-b) 1.241E+04 V·m
-c) 1.365E+04 V·m
+d) 1.502E+04 V·m
-e) 1.652E+04 V·m

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?

-a) 5.297E+00 N/C
-b) 5.827E+00 N/C
-c) 6.409E+00 N/C
-d) 7.050E+00 N/C
+e) 7.755E+00 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.740E+01 N·m2/C
-b) 1.914E+01 N·m2/C
-c) 2.106E+01 N·m2/C
-d) 2.316E+01 N·m2/C
+e) 2.548E+01 N·m2/C

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#### Key: D1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.989E+01 N·m2/C
-b) 6.588E+01 N·m2/C
-c) 7.247E+01 N·m2/C
+d) 7.971E+01 N·m2/C
-e) 8.769E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

-a) 7.054E+03 V·m
-b) 7.759E+03 V·m
-c) 8.535E+03 V·m
-d) 9.388E+03 V·m
+e) 1.033E+04 V·m

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?

-a) 9.642E+00 N/C
-b) 1.061E+01 N/C
+c) 1.167E+01 N/C
-d) 1.283E+01 N/C
-e) 1.412E+01 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.740E+01 N·m2/C
-b) 1.914E+01 N·m2/C
-c) 2.106E+01 N·m2/C
-d) 2.316E+01 N·m2/C
+e) 2.548E+01 N·m2/C

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#### Key: D2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.125E+01 N·m2/C
-b) 4.537E+01 N·m2/C
-c) 4.991E+01 N·m2/C
+d) 5.490E+01 N·m2/C
-e) 6.039E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.012E+01 N·m2/C
-b) 2.213E+01 N·m2/C
-c) 2.435E+01 N·m2/C
-d) 2.678E+01 N·m2/C
+e) 2.946E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

-a) 3.251E+01 N/C
-b) 3.577E+01 N/C
-c) 3.934E+01 N/C
-d) 4.328E+01 N/C
+e) 4.760E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

-a) 9.952E+03 V·m
-b) 1.095E+04 V·m
-c) 1.204E+04 V·m
+d) 1.325E+04 V·m
-e) 1.457E+04 V·m

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### Key: E0

1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?

+a) 7.825E+02 N/C
-b) 8.607E+02 N/C
-c) 9.468E+02 N/C
-d) 1.041E+03 N/C
-e) 1.146E+03 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.695E+01 N·m2/C
-b) 4.065E+01 N·m2/C
-c) 4.472E+01 N·m2/C
-d) 4.919E+01 N·m2/C
+e) 5.411E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.270E+01 N·m2/C
-b) 6.897E+01 N·m2/C
-c) 7.586E+01 N·m2/C
-d) 8.345E+01 N·m2/C
+e) 9.179E+01 N·m2/C

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#### Key: E1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.712E+01 N·m2/C
-b) 4.083E+01 N·m2/C
+c) 4.491E+01 N·m2/C
-d) 4.940E+01 N·m2/C
-e) 5.434E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

-a) 1.997E+03 V·m
+b) 2.197E+03 V·m
-c) 2.417E+03 V·m
-d) 2.659E+03 V·m
-e) 2.924E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 8.314E+01 N·m2/C
-b) 9.146E+01 N·m2/C
-c) 1.006E+02 N·m2/C
-d) 1.107E+02 N·m2/C
-e) 1.217E+02 N·m2/C

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

-a) 2.579E+02 N/C
+b) 2.837E+02 N/C
-c) 3.121E+02 N/C
-d) 3.433E+02 N/C
-e) 3.776E+02 N/C

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#### Key: E2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.989E+01 N·m2/C
-b) 6.588E+01 N·m2/C
-c) 7.247E+01 N·m2/C
+d) 7.971E+01 N·m2/C
-e) 8.769E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.924E+01 N·m2/C
-b) 4.316E+01 N·m2/C
-c) 4.748E+01 N·m2/C
+d) 5.222E+01 N·m2/C
-e) 5.745E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

-a) 7.054E+03 V·m
-b) 7.759E+03 V·m
-c) 8.535E+03 V·m
-d) 9.388E+03 V·m
+e) 1.033E+04 V·m

4) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

-a) 1.123E+02 N/C
-b) 1.235E+02 N/C
+c) 1.358E+02 N/C
-d) 1.494E+02 N/C
-e) 1.644E+02 N/C

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### Key: F0

1) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

-a) 1.123E+02 N/C
-b) 1.235E+02 N/C
+c) 1.358E+02 N/C
-d) 1.494E+02 N/C
-e) 1.644E+02 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?

+a) 9.592E+00 N/C
-b) 1.055E+01 N/C
-c) 1.161E+01 N/C
-d) 1.277E+01 N/C
-e) 1.404E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.777E+01 N·m2/C
-b) 5.254E+01 N·m2/C
-c) 5.780E+01 N·m2/C
+d) 6.358E+01 N·m2/C
-e) 6.993E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.3 m, z=z0=1.1 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 10 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.924E+01 N·m2/C
-b) 4.316E+01 N·m2/C
-c) 4.748E+01 N·m2/C
+d) 5.222E+01 N·m2/C
-e) 5.745E+01 N·m2/C

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#### Key: F1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.134E+01 N·m2/C
-b) 2.347E+01 N·m2/C
+c) 2.582E+01 N·m2/C
-d) 2.840E+01 N·m2/C
-e) 3.124E+01 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.6 m from the center of the shells?

-a) 6.641E+00 N/C
-b) 7.305E+00 N/C
+c) 8.036E+00 N/C
-d) 8.839E+00 N/C
-e) 9.723E+00 N/C

3) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

+a) 2.079E+02 N/C
-b) 2.287E+02 N/C
-c) 2.516E+02 N/C
-d) 2.767E+02 N/C
-e) 3.044E+02 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.992E+01 N·m2/C
-b) 2.192E+01 N·m2/C
+c) 2.411E+01 N·m2/C
-d) 2.652E+01 N·m2/C
-e) 2.917E+01 N·m2/C

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#### Key: F2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 8.415E+01 N·m2/C
-b) 9.256E+01 N·m2/C
-c) 1.018E+02 N·m2/C
+d) 1.120E+02 N·m2/C
-e) 1.232E+02 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

-a) 9.144E+00 N/C
-b) 1.006E+01 N/C
-c) 1.106E+01 N/C
-d) 1.217E+01 N/C
+e) 1.339E+01 N/C

3) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

+a) 3.604E+02 N/C
-b) 3.964E+02 N/C
-c) 4.360E+02 N/C
-d) 4.796E+02 N/C
-e) 5.276E+02 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.6 m, z=z0=1.2 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.3m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.809E+01 N·m2/C
-b) 5.290E+01 N·m2/C
+c) 5.819E+01 N·m2/C
-d) 6.401E+01 N·m2/C
-e) 7.041E+01 N·m2/C

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### Key: G0

1) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

-a) 2.274E+02 N/C
-b) 2.501E+02 N/C
+c) 2.751E+02 N/C
-d) 3.026E+02 N/C
-e) 3.329E+02 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.186E+01 N·m2/C
-b) 2.404E+01 N·m2/C
+c) 2.645E+01 N·m2/C
-d) 2.909E+01 N·m2/C
-e) 3.200E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

+a) 7.200E+01 V·m
-b) 7.920E+01 V·m
-c) 8.712E+01 V·m
-d) 9.583E+01 V·m
-e) 1.054E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.5 m, z=z0=1.5 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 9.8m2. Those in the xy plane have area 7.8m2 ,and those in the zx plane have area 9.8m2. An electric field has the xyz components (0, 6.1, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 5.978E+01 N·m2/C
-b) 6.576E+01 N·m2/C
-c) 7.233E+01 N·m2/C
-d) 7.957E+01 N·m2/C
-e) 8.752E+01 N·m2/C

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#### Key: G1

1) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

-a) 2.274E+02 N/C
-b) 2.501E+02 N/C
+c) 2.751E+02 N/C
-d) 3.026E+02 N/C
-e) 3.329E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

-a) 2.610E+03 V·m
-b) 2.871E+03 V·m
+c) 3.158E+03 V·m
-d) 3.474E+03 V·m
-e) 3.822E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.740E+01 N·m2/C
-b) 1.914E+01 N·m2/C
-c) 2.106E+01 N·m2/C
-d) 2.316E+01 N·m2/C
+e) 2.548E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.186E+01 N·m2/C
-b) 2.404E+01 N·m2/C
+c) 2.645E+01 N·m2/C
-d) 2.909E+01 N·m2/C
-e) 3.200E+01 N·m2/C

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#### Key: G2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 13.0m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 7.0, 5.7) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.953E+01 N·m2/C
-b) 5.449E+01 N·m2/C
-c) 5.993E+01 N·m2/C
-d) 6.593E+01 N·m2/C
+e) 7.252E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

-a) 1.997E+03 V·m
+b) 2.197E+03 V·m
-c) 2.417E+03 V·m
-d) 2.659E+03 V·m
-e) 2.924E+03 V·m

3) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?

+a) 4.782E+02 N/C
-b) 5.260E+02 N/C
-c) 5.787E+02 N/C
-d) 6.365E+02 N/C
-e) 7.002E+02 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.2 m, z=z0=1.1 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 6.7m2. An electric field of magnitude 16 N/C has components in the y and z directions and is directed at 53° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.420E+01 N·m2/C
-b) 4.862E+01 N·m2/C
-c) 5.348E+01 N·m2/C
-d) 5.882E+01 N·m2/C
+e) 6.471E+01 N·m2/C

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### Key: H0

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

+a) 3.337E+03 V·m
-b) 3.670E+03 V·m
-c) 4.037E+03 V·m
-d) 4.441E+03 V·m
-e) 4.885E+03 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.074E+01 N·m2/C
-b) 3.382E+01 N·m2/C
-c) 3.720E+01 N·m2/C
-d) 4.092E+01 N·m2/C
-e) 4.501E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.989E+01 N·m2/C
-b) 6.588E+01 N·m2/C
-c) 7.247E+01 N·m2/C
+d) 7.971E+01 N·m2/C
-e) 8.769E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 8.457E+01 N·m2/C
+b) 9.303E+01 N·m2/C
-c) 1.023E+02 N·m2/C
-d) 1.126E+02 N·m2/C
-e) 1.238E+02 N·m2/C

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#### Key: H1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=6), and (x=8, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{1.4}{\hat {i}}+2x^{2.3}{\hat {j}}+4y^{2.3}{\hat {k}}}$

-a) 2.694E+03 V·m
-b) 2.963E+03 V·m
-c) 3.259E+03 V·m
+d) 3.585E+03 V·m
-e) 3.944E+03 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.125E+01 N·m2/C
-b) 4.537E+01 N·m2/C
-c) 4.991E+01 N·m2/C
+d) 5.490E+01 N·m2/C
-e) 6.039E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.214E+01 N·m2/C
-b) 2.436E+01 N·m2/C
-c) 2.679E+01 N·m2/C
-d) 2.947E+01 N·m2/C
+e) 3.242E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.756E+01 N·m2/C
-b) 3.032E+01 N·m2/C
-c) 3.335E+01 N·m2/C
-d) 3.668E+01 N·m2/C
+e) 4.035E+01 N·m2/C

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#### Key: H2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

+a) 7.200E+01 V·m
-b) 7.920E+01 V·m
-c) 8.712E+01 V·m
-d) 9.583E+01 V·m
-e) 1.054E+02 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.6 m, z=z0=1.2 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.3m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 39° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.809E+01 N·m2/C
-b) 5.290E+01 N·m2/C
+c) 5.819E+01 N·m2/C
-d) 6.401E+01 N·m2/C
-e) 7.041E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 6.192E+01 N·m2/C
-b) 6.811E+01 N·m2/C
-c) 7.492E+01 N·m2/C
-d) 8.242E+01 N·m2/C
-e) 9.066E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 9.823E+00 N·m2/C
+b) 1.080E+01 N·m2/C
-c) 1.189E+01 N·m2/C
-d) 1.307E+01 N·m2/C
-e) 1.438E+01 N·m2/C

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### Key: I0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

+a) 5.058E+00 N/C
-b) 5.564E+00 N/C
-c) 6.120E+00 N/C
-d) 6.732E+00 N/C
-e) 7.405E+00 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

-a) 9.952E+03 V·m
-b) 1.095E+04 V·m
-c) 1.204E+04 V·m
+d) 1.325E+04 V·m
-e) 1.457E+04 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 6.5m2 ,and those in the zx plane have area 7.7m2. An electric field has the xyz components (0, 8.0, 9.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 6.192E+01 N·m2/C
-b) 6.811E+01 N·m2/C
-c) 7.492E+01 N·m2/C
-d) 8.242E+01 N·m2/C
-e) 9.066E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.134E+01 N·m2/C
-b) 2.347E+01 N·m2/C
+c) 2.582E+01 N·m2/C
-d) 2.840E+01 N·m2/C
-e) 3.124E+01 N·m2/C

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#### Key: I1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.3 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.5 m from the center of the shells?

-a) 1.994E+01 N/C
-b) 2.194E+01 N/C
-c) 2.413E+01 N/C
-d) 2.655E+01 N/C
+e) 2.920E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.3}{\hat {i}}+3x^{2.4}{\hat {j}}+2y^{1.8}{\hat {k}}}$

-a) 8.731E+02 V·m
-b) 9.604E+02 V·m
-c) 1.056E+03 V·m
+d) 1.162E+03 V·m
-e) 1.278E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.6 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 7.8m2. An electric field has the xyz components (0, 8.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.000E+01 N·m2/C
-b) 5.500E+01 N·m2/C
-c) 6.050E+01 N·m2/C
+d) 6.656E+01 N·m2/C
-e) 7.321E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.134E+01 N·m2/C
-b) 2.347E+01 N·m2/C
+c) 2.582E+01 N·m2/C
-d) 2.840E+01 N·m2/C
-e) 3.124E+01 N·m2/C

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#### Key: I2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.777E+01 N·m2/C
-b) 5.254E+01 N·m2/C
-c) 5.780E+01 N·m2/C
+d) 6.358E+01 N·m2/C
-e) 6.993E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.730E+01 N·m2/C
+b) 5.203E+01 N·m2/C
-c) 5.723E+01 N·m2/C
-d) 6.295E+01 N·m2/C
-e) 6.925E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?

-a) 5.297E+00 N/C
-b) 5.827E+00 N/C
-c) 6.409E+00 N/C
-d) 7.050E+00 N/C
+e) 7.755E+00 N/C

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### Key: J0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?

-a) 8.580E+00 N/C
-b) 9.438E+00 N/C
-c) 1.038E+01 N/C
+d) 1.142E+01 N/C
-e) 1.256E+01 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.8}{\hat {i}}+3x^{2.8}{\hat {j}}+2y^{2.4}{\hat {k}}}$

-a) 1.997E+03 V·m
+b) 2.197E+03 V·m
-c) 2.417E+03 V·m
-d) 2.659E+03 V·m
-e) 2.924E+03 V·m

3) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 3.0 m from the center?

+a) 7.825E+02 N/C
-b) 8.607E+02 N/C
-c) 9.468E+02 N/C
-d) 1.041E+03 N/C
-e) 1.146E+03 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.891E+01 N·m2/C
-b) 2.080E+01 N·m2/C
+c) 2.288E+01 N·m2/C
-d) 2.517E+01 N·m2/C
-e) 2.768E+01 N·m2/C

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#### Key: J1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

-a) 8.545E+01 V·m
-b) 9.400E+01 V·m
-c) 1.034E+02 V·m
-d) 1.137E+02 V·m
+e) 1.251E+02 V·m

2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.7 (r≤R) where a=3 nC·m-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 1.390E+03 N/C
+b) 1.530E+03 N/C
-c) 1.682E+03 N/C
-d) 1.851E+03 N/C
-e) 2.036E+03 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.074E+01 N·m2/C
-b) 3.382E+01 N·m2/C
-c) 3.720E+01 N·m2/C
-d) 4.092E+01 N·m2/C
-e) 4.501E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

-a) 2.988E+00 N/C
-b) 3.287E+00 N/C
-c) 3.616E+00 N/C
-d) 3.977E+00 N/C
+e) 4.375E+00 N/C

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#### Key: J2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

+a) 5.058E+00 N/C
-b) 5.564E+00 N/C
-c) 6.120E+00 N/C
-d) 6.732E+00 N/C
-e) 7.405E+00 N/C

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

+a) 2.079E+02 N/C
-b) 2.287E+02 N/C
-c) 2.516E+02 N/C
-d) 2.767E+02 N/C
-e) 3.044E+02 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.6 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 7.8m2. An electric field has the xyz components (0, 8.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.000E+01 N·m2/C
-b) 5.500E+01 N·m2/C
-c) 6.050E+01 N·m2/C
+d) 6.656E+01 N·m2/C
-e) 7.321E+01 N·m2/C

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### Key: K0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.730E+01 N·m2/C
+b) 5.203E+01 N·m2/C
-c) 5.723E+01 N·m2/C
-d) 6.295E+01 N·m2/C
-e) 6.925E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.270E+01 N·m2/C
-b) 6.897E+01 N·m2/C
-c) 7.586E+01 N·m2/C
-d) 8.345E+01 N·m2/C
+e) 9.179E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

-a) 2.067E+03 V·m
-b) 2.274E+03 V·m
+c) 2.501E+03 V·m
-d) 2.752E+03 V·m
-e) 3.027E+03 V·m

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?

-a) 1.096E+00 N/C
-b) 1.206E+00 N/C
-c) 1.327E+00 N/C
-d) 1.459E+00 N/C
+e) 1.605E+00 N/C

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#### Key: K1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5.6 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.6 m from the center of the shells?

-a) 9.642E+00 N/C
-b) 1.061E+01 N/C
+c) 1.167E+01 N/C
-d) 1.283E+01 N/C
-e) 1.412E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.074E+01 N·m2/C
-b) 3.382E+01 N·m2/C
-c) 3.720E+01 N·m2/C
-d) 4.092E+01 N·m2/C
-e) 4.501E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 9.823E+00 N·m2/C
+b) 1.080E+01 N·m2/C
-c) 1.189E+01 N·m2/C
-d) 1.307E+01 N·m2/C
-e) 1.438E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

-a) 9.952E+03 V·m
-b) 1.095E+04 V·m
-c) 1.204E+04 V·m
+d) 1.325E+04 V·m
-e) 1.457E+04 V·m

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#### Key: K2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

-a) 1.128E+04 V·m
-b) 1.241E+04 V·m
-c) 1.365E+04 V·m
+d) 1.502E+04 V·m
-e) 1.652E+04 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.8 m, z=z0=1.9 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 8.0m2 ,and those in the zx plane have area 8.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.662E+01 N·m2/C
+b) 4.028E+01 N·m2/C
-c) 4.430E+01 N·m2/C
-d) 4.873E+01 N·m2/C
-e) 5.361E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.9 nano-Coulombs. What is the magnitude of the electric field at a distance of 2.1 m from the center of the shells?

-a) 5.297E+00 N/C
-b) 5.827E+00 N/C
-c) 6.409E+00 N/C
-d) 7.050E+00 N/C
+e) 7.755E+00 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.074E+01 N·m2/C
-b) 3.382E+01 N·m2/C
-c) 3.720E+01 N·m2/C
-d) 4.092E+01 N·m2/C
-e) 4.501E+01 N·m2/C

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### Key: L0

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

-a) 7.054E+03 V·m
-b) 7.759E+03 V·m
-c) 8.535E+03 V·m
-d) 9.388E+03 V·m
+e) 1.033E+04 V·m

2) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

+a) 3.604E+02 N/C
-b) 3.964E+02 N/C
-c) 4.360E+02 N/C
-d) 4.796E+02 N/C
-e) 5.276E+02 N/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

-a) 2.837E+01 N/C
-b) 3.121E+01 N/C
-c) 3.433E+01 N/C
-d) 3.776E+01 N/C
+e) 4.154E+01 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.777E+01 N·m2/C
-b) 5.254E+01 N·m2/C
-c) 5.780E+01 N·m2/C
+d) 6.358E+01 N·m2/C
-e) 6.993E+01 N·m2/C

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#### Key: L1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

-a) 2.610E+03 V·m
-b) 2.871E+03 V·m
+c) 3.158E+03 V·m
-d) 3.474E+03 V·m
-e) 3.822E+03 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.012E+01 N·m2/C
-b) 2.213E+01 N·m2/C
-c) 2.435E+01 N·m2/C
-d) 2.678E+01 N·m2/C
+e) 2.946E+01 N·m2/C

3) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

-a) 3.821E+02 N/C
-b) 4.203E+02 N/C
-c) 4.624E+02 N/C
+d) 5.086E+02 N/C
-e) 5.594E+02 N/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

-a) 9.144E+00 N/C
-b) 1.006E+01 N/C
-c) 1.106E+01 N/C
-d) 1.217E+01 N/C
+e) 1.339E+01 N/C

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#### Key: L2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.9}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.5}{\hat {k}}}$

-a) 4.286E+03 V·m
-b) 4.714E+03 V·m
+c) 5.186E+03 V·m
-d) 5.704E+03 V·m
-e) 6.275E+03 V·m

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

+a) 5.058E+00 N/C
-b) 5.564E+00 N/C
-c) 6.120E+00 N/C
-d) 6.732E+00 N/C
-e) 7.405E+00 N/C

3) A non-conducting sphere of radius R=3.3 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 1.5 m from the center?

-a) 1.123E+02 N/C
-b) 1.235E+02 N/C
+c) 1.358E+02 N/C
-d) 1.494E+02 N/C
-e) 1.644E+02 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.270E+01 N·m2/C
-b) 6.897E+01 N·m2/C
-c) 7.586E+01 N·m2/C
-d) 8.345E+01 N·m2/C
+e) 9.179E+01 N·m2/C

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### Key: M0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.9 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.1 m, z=z0=1.3 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 6.5m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 5.385E+01 N·m2/C
-b) 5.923E+01 N·m2/C
-c) 6.516E+01 N·m2/C
-d) 7.167E+01 N·m2/C
-e) 7.884E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.750E+01 N·m2/C
-b) 4.125E+01 N·m2/C
-c) 4.537E+01 N·m2/C
+d) 4.991E+01 N·m2/C
-e) 5.490E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.740E+01 N·m2/C
-b) 1.914E+01 N·m2/C
-c) 2.106E+01 N·m2/C
-d) 2.316E+01 N·m2/C
+e) 2.548E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.5 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

-a) 2.601E+01 N/C
-b) 2.861E+01 N/C
-c) 3.147E+01 N/C
+d) 3.462E+01 N/C
-e) 3.808E+01 N/C

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#### Key: M1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.6 m, z=z0=1.4 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.959E+01 N·m2/C
-b) 4.354E+01 N·m2/C
-c) 4.790E+01 N·m2/C
+d) 5.269E+01 N·m2/C
-e) 5.796E+01 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

-a) 3.251E+01 N/C
-b) 3.577E+01 N/C
-c) 3.934E+01 N/C
-d) 4.328E+01 N/C
+e) 4.760E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.698E+01 N·m2/C
-b) 1.868E+01 N·m2/C
-c) 2.055E+01 N·m2/C
-d) 2.260E+01 N·m2/C
+e) 2.486E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.614E+01 N·m2/C
+b) 7.275E+01 N·m2/C
-c) 8.003E+01 N·m2/C
-d) 8.803E+01 N·m2/C
-e) 9.683E+01 N·m2/C

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#### Key: M2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

-a) 3.251E+01 N/C
-b) 3.577E+01 N/C
-c) 3.934E+01 N/C
-d) 4.328E+01 N/C
+e) 4.760E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.901E+01 N·m2/C
-b) 3.192E+01 N·m2/C
-c) 3.511E+01 N·m2/C
-d) 3.862E+01 N·m2/C
+e) 4.248E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.9 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 6.8m2 ,and those in the zx plane have area 7.7m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 57° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.898E+01 N·m2/C
+b) 7.588E+01 N·m2/C
-c) 8.347E+01 N·m2/C
-d) 9.181E+01 N·m2/C
-e) 1.010E+02 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.989E+01 N·m2/C
-b) 6.588E+01 N·m2/C
-c) 7.247E+01 N·m2/C
+d) 7.971E+01 N·m2/C
-e) 8.769E+01 N·m2/C

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### Key: N0

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

-a) 1.491E+01 N/C
-b) 1.640E+01 N/C
+c) 1.804E+01 N/C
-d) 1.984E+01 N/C
-e) 2.182E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.6 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 7.8m2. An electric field has the xyz components (0, 8.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.000E+01 N·m2/C
-b) 5.500E+01 N·m2/C
-c) 6.050E+01 N·m2/C
+d) 6.656E+01 N·m2/C
-e) 7.321E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.756E+01 N·m2/C
-b) 3.032E+01 N·m2/C
-c) 3.335E+01 N·m2/C
-d) 3.668E+01 N·m2/C
+e) 4.035E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}}$

-a) 1.206E+03 V·m
+b) 1.326E+03 V·m
-c) 1.459E+03 V·m
-d) 1.605E+03 V·m
-e) 1.765E+03 V·m

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#### Key: N1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.3 m, z=z0=1.3 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 5.7m2. An electric field has the xyz components (0, 5.7, 7.5) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.249E+01 N·m2/C
-b) 3.574E+01 N·m2/C
-c) 3.931E+01 N·m2/C
-d) 4.324E+01 N·m2/C
-e) 4.757E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=5), and (x=6, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{1.7}{\hat {i}}+3x^{1.6}{\hat {j}}+4y^{2.7}{\hat {k}}}$

-a) 2.067E+03 V·m
-b) 2.274E+03 V·m
+c) 2.501E+03 V·m
-d) 2.752E+03 V·m
-e) 3.027E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.012E+01 N·m2/C
-b) 2.213E+01 N·m2/C
-c) 2.435E+01 N·m2/C
-d) 2.678E+01 N·m2/C
+e) 2.946E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?

+a) 9.592E+00 N/C
-b) 1.055E+01 N/C
-c) 1.161E+01 N/C
-d) 1.277E+01 N/C
-e) 1.404E+01 N/C

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#### Key: N2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.756E+01 N·m2/C
-b) 3.032E+01 N·m2/C
-c) 3.335E+01 N·m2/C
-d) 3.668E+01 N·m2/C
+e) 4.035E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.740E+01 N·m2/C
-b) 1.914E+01 N·m2/C
-c) 2.106E+01 N·m2/C
-d) 2.316E+01 N·m2/C
+e) 2.548E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 1.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8 m from the center of the shells?

-a) 1.096E+00 N/C
-b) 1.206E+00 N/C
-c) 1.327E+00 N/C
-d) 1.459E+00 N/C
+e) 1.605E+00 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

-a) 7.054E+03 V·m
-b) 7.759E+03 V·m
-c) 8.535E+03 V·m
-d) 9.388E+03 V·m
+e) 1.033E+04 V·m

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### Key: O0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.891E+01 N·m2/C
-b) 2.080E+01 N·m2/C
+c) 2.288E+01 N·m2/C
-d) 2.517E+01 N·m2/C
-e) 2.768E+01 N·m2/C

2) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

-a) 2.579E+02 N/C
+b) 2.837E+02 N/C
-c) 3.121E+02 N/C
-d) 3.433E+02 N/C
-e) 3.776E+02 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

-a) 9.952E+03 V·m
-b) 1.095E+04 V·m
-c) 1.204E+04 V·m
+d) 1.325E+04 V·m
-e) 1.457E+04 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.5 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 8.3m2. Those in the xy plane have area 5.7m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.408E+01 N·m2/C
+b) 5.949E+01 N·m2/C
-c) 6.544E+01 N·m2/C
-d) 7.198E+01 N·m2/C
-e) 7.918E+01 N·m2/C

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#### Key: O1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.6 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 7.8m2. An electric field has the xyz components (0, 8.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.000E+01 N·m2/C
-b) 5.500E+01 N·m2/C
-c) 6.050E+01 N·m2/C
+d) 6.656E+01 N·m2/C
-e) 7.321E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.737E+01 N·m2/C
-b) 1.910E+01 N·m2/C
-c) 2.101E+01 N·m2/C
-d) 2.311E+01 N·m2/C
+e) 2.543E+01 N·m2/C

3) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 6.411E+02 N/C
-b) 7.052E+02 N/C
+c) 7.757E+02 N/C
-d) 8.533E+02 N/C
-e) 9.386E+02 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

+a) 3.337E+03 V·m
-b) 3.670E+03 V·m
-c) 4.037E+03 V·m
-d) 4.441E+03 V·m
-e) 4.885E+03 V·m

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#### Key: O2

1) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.3 m from the center?

-a) 2.777E+02 N/C
-b) 3.055E+02 N/C
+c) 3.361E+02 N/C
-d) 3.697E+02 N/C
-e) 4.066E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

+a) 7.200E+01 V·m
-b) 7.920E+01 V·m
-c) 8.712E+01 V·m
-d) 9.583E+01 V·m
-e) 1.054E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.0 m, z=z0=1.9 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.9m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 2.9m2. An electric field has the xyz components (0, 5.3, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.388E+01 N·m2/C
+b) 1.526E+01 N·m2/C
-c) 1.679E+01 N·m2/C
-d) 1.847E+01 N·m2/C
-e) 2.032E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.6m2 ,and those in the zx plane have area 13.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 46° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.988E+01 N·m2/C
-b) 5.487E+01 N·m2/C
-c) 6.035E+01 N·m2/C
-d) 6.639E+01 N·m2/C
+e) 7.303E+01 N·m2/C

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### Key: P0

1) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.5 m from the center?

+a) 1.383E+02 N/C
-b) 1.522E+02 N/C
-c) 1.674E+02 N/C
-d) 1.841E+02 N/C
-e) 2.025E+02 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

-a) 2.210E+04 V·m
+b) 2.431E+04 V·m
-c) 2.674E+04 V·m
-d) 2.941E+04 V·m
-e) 3.235E+04 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.695E+01 N·m2/C
-b) 4.065E+01 N·m2/C
-c) 4.472E+01 N·m2/C
-d) 4.919E+01 N·m2/C
+e) 5.411E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.6 m, z=z0=1.4 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.959E+01 N·m2/C
-b) 4.354E+01 N·m2/C
-c) 4.790E+01 N·m2/C
+d) 5.269E+01 N·m2/C
-e) 5.796E+01 N·m2/C

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#### Key: P1

1) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.7 (r≤R) where a=3 nC·m-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 1.390E+03 N/C
+b) 1.530E+03 N/C
-c) 1.682E+03 N/C
-d) 1.851E+03 N/C
-e) 2.036E+03 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.9 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 12.0m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.737E+01 N·m2/C
-b) 1.910E+01 N·m2/C
-c) 2.101E+01 N·m2/C
-d) 2.311E+01 N·m2/C
+e) 2.543E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 7.876E+01 N·m2/C
-b) 8.664E+01 N·m2/C
-c) 9.531E+01 N·m2/C
-d) 1.048E+02 N·m2/C
-e) 1.153E+02 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

-a) 9.952E+03 V·m
-b) 1.095E+04 V·m
-c) 1.204E+04 V·m
+d) 1.325E+04 V·m
-e) 1.457E+04 V·m

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#### Key: P2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.012E+01 N·m2/C
-b) 2.213E+01 N·m2/C
-c) 2.435E+01 N·m2/C
-d) 2.678E+01 N·m2/C
+e) 2.946E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.698E+01 N·m2/C
-b) 1.868E+01 N·m2/C
-c) 2.055E+01 N·m2/C
-d) 2.260E+01 N·m2/C
+e) 2.486E+01 N·m2/C

3) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

+a) 3.604E+02 N/C
-b) 3.964E+02 N/C
-c) 4.360E+02 N/C
-d) 4.796E+02 N/C
-e) 5.276E+02 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

+a) 3.429E+03 V·m
-b) 3.771E+03 V·m
-c) 4.149E+03 V·m
-d) 4.564E+03 V·m
-e) 5.020E+03 V·m

Click these links for the keys:

### Key: Q0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.270E+01 N·m2/C
-b) 6.897E+01 N·m2/C
-c) 7.586E+01 N·m2/C
-d) 8.345E+01 N·m2/C
+e) 9.179E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.730E+01 N·m2/C
+b) 5.203E+01 N·m2/C
-c) 5.723E+01 N·m2/C
-d) 6.295E+01 N·m2/C
-e) 6.925E+01 N·m2/C

4) A non-conducting sphere of radius R=2.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=3 nC·m-1.5. What is the magnitude of the electric field at a distance of 1.7 m from the center?

-a) 2.579E+02 N/C
+b) 2.837E+02 N/C
-c) 3.121E+02 N/C
-d) 3.433E+02 N/C
-e) 3.776E+02 N/C

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#### Key: Q1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

-a) 2.610E+03 V·m
-b) 2.871E+03 V·m
+c) 3.158E+03 V·m
-d) 3.474E+03 V·m
-e) 3.822E+03 V·m

2) A non-conducting sphere of radius R=1.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 0.73 m from the center?

+a) 2.285E+01 N/C
-b) 2.514E+01 N/C
-c) 2.765E+01 N/C
-d) 3.042E+01 N/C
-e) 3.346E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.891E+01 N·m2/C
-b) 2.080E+01 N·m2/C
+c) 2.288E+01 N·m2/C
-d) 2.517E+01 N·m2/C
-e) 2.768E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.7 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=5.9 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.6m2 ,and those in the zx plane have area 13.0m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 46° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.988E+01 N·m2/C
-b) 5.487E+01 N·m2/C
-c) 6.035E+01 N·m2/C
-d) 6.639E+01 N·m2/C
+e) 7.303E+01 N·m2/C

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#### Key: Q2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.3 m, and z=z1=5.2 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 12 N/C has components in the y and z directions and is directed at 49° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.777E+01 N·m2/C
-b) 5.254E+01 N·m2/C
-c) 5.780E+01 N·m2/C
+d) 6.358E+01 N·m2/C
-e) 6.993E+01 N·m2/C

2) A non-conducting sphere of radius R=3.1 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.7 m from the center?

+a) 4.782E+02 N/C
-b) 5.260E+02 N/C
-c) 5.787E+02 N/C
-d) 6.365E+02 N/C
-e) 7.002E+02 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.125E+01 N·m2/C
-b) 4.537E+01 N·m2/C
-c) 4.991E+01 N·m2/C
+d) 5.490E+01 N·m2/C
-e) 6.039E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

+a) 7.200E+01 V·m
-b) 7.920E+01 V·m
-c) 8.712E+01 V·m
-d) 9.583E+01 V·m
-e) 1.054E+02 V·m

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### Key: R0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=4.3 m, z=z0=1.5 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 8.3m2. Those in the xy plane have area 5.7m2 ,and those in the zx plane have area 7.0m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 28° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.408E+01 N·m2/C
+b) 5.949E+01 N·m2/C
-c) 6.544E+01 N·m2/C
-d) 7.198E+01 N·m2/C
-e) 7.918E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.3}{\hat {i}}+3x^{2.4}{\hat {j}}+2y^{1.8}{\hat {k}}}$

-a) 8.731E+02 V·m
-b) 9.604E+02 V·m
-c) 1.056E+03 V·m
+d) 1.162E+03 V·m
-e) 1.278E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=4.3 m, z=z0=1.3 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 4.0m2 ,and those in the zx plane have area 5.7m2. An electric field has the xyz components (0, 5.7, 7.5) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.249E+01 N·m2/C
-b) 3.574E+01 N·m2/C
-c) 3.931E+01 N·m2/C
-d) 4.324E+01 N·m2/C
-e) 4.757E+01 N·m2/C

4) A non-conducting sphere of radius R=1.2 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.6 (r≤R) where a=2 nC·m-1.4. What is the magnitude of the electric field at a distance of 0.76 m from the center?

+a) 2.406E+01 N/C
-b) 2.646E+01 N/C
-c) 2.911E+01 N/C
-d) 3.202E+01 N/C
-e) 3.522E+01 N/C

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#### Key: R1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.740E+01 N·m2/C
-b) 1.914E+01 N·m2/C
-c) 2.106E+01 N·m2/C
-d) 2.316E+01 N·m2/C
+e) 2.548E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.439E+01 N·m2/C
-b) 5.983E+01 N·m2/C
-c) 6.581E+01 N·m2/C
+d) 7.239E+01 N·m2/C
-e) 7.963E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m

4) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 6.411E+02 N/C
-b) 7.052E+02 N/C
+c) 7.757E+02 N/C
-d) 8.533E+02 N/C
-e) 9.386E+02 N/C

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#### Key: R2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

+a) 2.079E+02 N/C
-b) 2.287E+02 N/C
-c) 2.516E+02 N/C
-d) 2.767E+02 N/C
-e) 3.044E+02 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 8.314E+01 N·m2/C
-b) 9.146E+01 N·m2/C
-c) 1.006E+02 N·m2/C
-d) 1.107E+02 N·m2/C
-e) 1.217E+02 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 8.9m2 ,and those in the zx plane have area 7.2m2. An electric field has the xyz components (0, 5.9, 8.9) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.901E+01 N·m2/C
-b) 3.192E+01 N·m2/C
-c) 3.511E+01 N·m2/C
-d) 3.862E+01 N·m2/C
+e) 4.248E+01 N·m2/C

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### Key: S0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.992E+01 N·m2/C
-b) 2.192E+01 N·m2/C
+c) 2.411E+01 N·m2/C
-d) 2.652E+01 N·m2/C
-e) 2.917E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.891E+01 N·m2/C
-b) 2.080E+01 N·m2/C
+c) 2.288E+01 N·m2/C
-d) 2.517E+01 N·m2/C
-e) 2.768E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=6), and (x=7, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.5}{\hat {i}}+3x^{1.8}{\hat {j}}+2y^{2.8}{\hat {k}}}$

+a) 3.337E+03 V·m
-b) 3.670E+03 V·m
-c) 4.037E+03 V·m
-d) 4.441E+03 V·m
-e) 4.885E+03 V·m

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?

-a) 8.580E+00 N/C
-b) 9.438E+00 N/C
-c) 1.038E+01 N/C
+d) 1.142E+01 N/C
-e) 1.256E+01 N/C

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#### Key: S1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=9, y=0), (x=0, y=9), and (x=9, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.8}{\hat {i}}+1x^{2.3}{\hat {j}}+2y^{2.9}{\hat {k}}}$

-a) 2.210E+04 V·m
+b) 2.431E+04 V·m
-c) 2.674E+04 V·m
-d) 2.941E+04 V·m
-e) 3.235E+04 V·m

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

-a) 2.964E+00 N/C
-b) 3.260E+00 N/C
-c) 3.586E+00 N/C
+d) 3.944E+00 N/C
-e) 4.339E+00 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.2 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 6.0m2. An electric field has the xyz components (0, 8.7, 8.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.730E+01 N·m2/C
+b) 5.203E+01 N·m2/C
-c) 5.723E+01 N·m2/C
-d) 6.295E+01 N·m2/C
-e) 6.925E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=4.3 m, z=z0=1.7 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 4.1m2 ,and those in the zx plane have area 6.8m2. An electric field of magnitude 13 N/C has components in the y and z directions and is directed at 27° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 7.876E+01 N·m2/C
-b) 8.664E+01 N·m2/C
-c) 9.531E+01 N·m2/C
-d) 1.048E+02 N·m2/C
-e) 1.153E+02 N·m2/C

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#### Key: S2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

-a) 1.114E+01 N/C
+b) 1.225E+01 N/C
-c) 1.347E+01 N/C
-d) 1.482E+01 N/C
-e) 1.630E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.920E+01 N·m2/C
-b) 7.612E+01 N·m2/C
-c) 8.373E+01 N·m2/C
+d) 9.210E+01 N·m2/C
-e) 1.013E+02 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.125E+01 N·m2/C
-b) 4.537E+01 N·m2/C
-c) 4.991E+01 N·m2/C
+d) 5.490E+01 N·m2/C
-e) 6.039E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.0}{\hat {i}}+2x^{2.1}{\hat {j}}+3y^{2.5}{\hat {k}}}$

-a) 9.027E+03 V·m
+b) 9.930E+03 V·m
-c) 1.092E+04 V·m
-d) 1.202E+04 V·m
-e) 1.322E+04 V·m

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### Key: T0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.3 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.0m2. Those in the xy plane have area 6.2m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 32° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.695E+01 N·m2/C
-b) 4.065E+01 N·m2/C
-c) 4.472E+01 N·m2/C
-d) 4.919E+01 N·m2/C
+e) 5.411E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.4 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 5.0m2 ,and those in the zx plane have area 6.6m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 34° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.756E+01 N·m2/C
-b) 3.032E+01 N·m2/C
-c) 3.335E+01 N·m2/C
-d) 3.668E+01 N·m2/C
+e) 4.035E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 5.5, 7.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.891E+01 N·m2/C
-b) 2.080E+01 N·m2/C
+c) 2.288E+01 N·m2/C
-d) 2.517E+01 N·m2/C
-e) 2.768E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.0}{\hat {i}}+2x^{2.1}{\hat {j}}+3y^{2.5}{\hat {k}}}$

-a) 9.027E+03 V·m
+b) 9.930E+03 V·m
-c) 1.092E+04 V·m
-d) 1.202E+04 V·m
-e) 1.322E+04 V·m

Click these links for the keys:

#### Key: T1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.712E+01 N·m2/C
-b) 4.083E+01 N·m2/C
+c) 4.491E+01 N·m2/C
-d) 4.940E+01 N·m2/C
-e) 5.434E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.8 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 9.2m2 ,and those in the zx plane have area 8.1m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 32° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.134E+01 N·m2/C
-b) 2.347E+01 N·m2/C
+c) 2.582E+01 N·m2/C
-d) 2.840E+01 N·m2/C
-e) 3.124E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=4.2 m, z=z0=1.9 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 10.0m2. Those in the xy plane have area 8.1m2 ,and those in the zx plane have area 10.0m2. An electric field has the xyz components (0, 8.5, 6.4) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 7.081E+01 N·m2/C
-b) 7.789E+01 N·m2/C
+c) 8.568E+01 N·m2/C
-d) 9.425E+01 N·m2/C
-e) 1.037E+02 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m

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#### Key: T2

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=9), and (x=4, y=9), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.2}{\hat {i}}+1x^{3.3}{\hat {j}}+5y^{2.4}{\hat {k}}}$

-a) 7.054E+03 V·m
-b) 7.759E+03 V·m
-c) 8.535E+03 V·m
-d) 9.388E+03 V·m
+e) 1.033E+04 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 8.921E+01 N·m2/C
-b) 9.813E+01 N·m2/C
-c) 1.079E+02 N·m2/C
-d) 1.187E+02 N·m2/C
-e) 1.306E+02 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.8 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 3.9m2 ,and those in the zx plane have area 4.3m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 31° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.521E+01 N·m2/C
-b) 4.973E+01 N·m2/C
-c) 5.470E+01 N·m2/C
-d) 6.017E+01 N·m2/C
+e) 6.619E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.7 m, z=z0=1.2 m, and z=z1=4.1 m. The surfaces in the yz plane each have area 9.6m2. Those in the xy plane have area 6.6m2 ,and those in the zx plane have area 5.8m2. An electric field has the xyz components (0, 8.4, 5.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.328E+01 N·m2/C
-b) 3.660E+01 N·m2/C
-c) 4.026E+01 N·m2/C
-d) 4.429E+01 N·m2/C
+e) 4.872E+01 N·m2/C

Click these links for the keys:

### Key: U0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.4 m, z=z0=1.4 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 9.6m2 ,and those in the zx plane have area 11.0m2. An electric field of magnitude 15 N/C has components in the y and z directions and is directed at 33° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 8.921E+01 N·m2/C
-b) 9.813E+01 N·m2/C
-c) 1.079E+02 N·m2/C
-d) 1.187E+02 N·m2/C
-e) 1.306E+02 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.8 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 3.9m2 ,and those in the zx plane have area 4.3m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 31° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.521E+01 N·m2/C
-b) 4.973E+01 N·m2/C
-c) 5.470E+01 N·m2/C
-d) 6.017E+01 N·m2/C
+e) 6.619E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

-a) 1.491E+01 N/C
-b) 1.640E+01 N/C
+c) 1.804E+01 N/C
-d) 1.984E+01 N/C
-e) 2.182E+01 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

+a) 3.429E+03 V·m
-b) 3.771E+03 V·m
-c) 4.149E+03 V·m
-d) 4.564E+03 V·m
-e) 5.020E+03 V·m

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#### Key: U1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.012E+01 N·m2/C
-b) 2.213E+01 N·m2/C
-c) 2.435E+01 N·m2/C
-d) 2.678E+01 N·m2/C
+e) 2.946E+01 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

-a) 2.964E+00 N/C
-b) 3.260E+00 N/C
-c) 3.586E+00 N/C
+d) 3.944E+00 N/C
-e) 4.339E+00 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=3), and (x=4, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.7}{\hat {i}}+2x^{2.9}{\hat {j}}+2y^{2.0}{\hat {k}}}$

+a) 7.200E+01 V·m
-b) 7.920E+01 V·m
-c) 8.712E+01 V·m
-d) 9.583E+01 V·m
-e) 1.054E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.8 m, z=z0=1.3 m, and z=z1=4.4 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 9.8m2 ,and those in the zx plane have area 7.4m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 46° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 8.457E+01 N·m2/C
+b) 9.303E+01 N·m2/C
-c) 1.023E+02 N·m2/C
-d) 1.126E+02 N·m2/C
-e) 1.238E+02 N·m2/C

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#### Key: U2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 8.415E+01 N·m2/C
-b) 9.256E+01 N·m2/C
-c) 1.018E+02 N·m2/C
+d) 1.120E+02 N·m2/C
-e) 1.232E+02 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 9.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.4 m from the center of the shells?

-a) 1.491E+01 N/C
-b) 1.640E+01 N/C
+c) 1.804E+01 N/C
-d) 1.984E+01 N/C
-e) 2.182E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.1 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.8 m, and z=z1=5.7 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 3.9m2 ,and those in the zx plane have area 4.3m2. An electric field of magnitude 18 N/C has components in the y and z directions and is directed at 31° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.521E+01 N·m2/C
-b) 4.973E+01 N·m2/C
-c) 5.470E+01 N·m2/C
-d) 6.017E+01 N·m2/C
+e) 6.619E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=6), and (x=6, y=6), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{1.8}{\hat {i}}+3x^{1.9}{\hat {j}}+5y^{3.2}{\hat {k}}}$

-a) 9.952E+03 V·m
-b) 1.095E+04 V·m
-c) 1.204E+04 V·m
+d) 1.325E+04 V·m
-e) 1.457E+04 V·m

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### Key: V0

1) A non-conducting sphere of radius R=3.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.5 (r≤R) where a=2 nC·m-1.5. What is the magnitude of the electric field at a distance of 2.2 m from the center?

+a) 3.604E+02 N/C
-b) 3.964E+02 N/C
-c) 4.360E+02 N/C
-d) 4.796E+02 N/C
-e) 5.276E+02 N/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

+a) 5.058E+00 N/C
-b) 5.564E+00 N/C
-c) 6.120E+00 N/C
-d) 6.732E+00 N/C
-e) 7.405E+00 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 8.415E+01 N·m2/C
-b) 9.256E+01 N·m2/C
-c) 1.018E+02 N·m2/C
+d) 1.120E+02 N·m2/C
-e) 1.232E+02 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.8 m, z=z0=1.2 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 17.0m2. Those in the xy plane have area 6.4m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 25° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.992E+01 N·m2/C
-b) 2.192E+01 N·m2/C
+c) 2.411E+01 N·m2/C
-d) 2.652E+01 N·m2/C
-e) 2.917E+01 N·m2/C

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#### Key: V1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.214E+01 N·m2/C
-b) 2.436E+01 N·m2/C
-c) 2.679E+01 N·m2/C
-d) 2.947E+01 N·m2/C
+e) 3.242E+01 N·m2/C

2) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

+a) 3.797E+01 N/C
-b) 4.177E+01 N/C
-c) 4.595E+01 N/C
-d) 5.054E+01 N/C
-e) 5.560E+01 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.7 m, z=z0=1.9 m, and z=z1=5.4 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 11.0m2 ,and those in the zx plane have area 8.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 26° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.012E+01 N·m2/C
-b) 2.213E+01 N·m2/C
-c) 2.435E+01 N·m2/C
-d) 2.678E+01 N·m2/C
+e) 2.946E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 3.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.5 m from the center of the shells?

+a) 5.058E+00 N/C
-b) 5.564E+00 N/C
-c) 6.120E+00 N/C
-d) 6.732E+00 N/C
-e) 7.405E+00 N/C

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#### Key: V2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.1 m. The other four surfaces are rectangles in y=y0=1.7 m, y=y1=5.6 m, z=z0=1.8 m, and z=z1=4.2 m. The surfaces in the yz plane each have area 9.4m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 5.0m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 29° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.186E+01 N·m2/C
-b) 2.404E+01 N·m2/C
+c) 2.645E+01 N·m2/C
-d) 2.909E+01 N·m2/C
-e) 3.200E+01 N·m2/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.1 m, y=y1=5.7 m, z=z0=1.8 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.5m2. An electric field of magnitude 5 N/C has components in the y and z directions and is directed at 38° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 9.823E+00 N·m2/C
+b) 1.080E+01 N·m2/C
-c) 1.189E+01 N·m2/C
-d) 1.307E+01 N·m2/C
-e) 1.438E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.0 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.7 m from the center of the shells?

-a) 2.964E+00 N/C
-b) 3.260E+00 N/C
-c) 3.586E+00 N/C
+d) 3.944E+00 N/C
-e) 4.339E+00 N/C

4) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=3 nC·m-1.8. What is the magnitude of the electric field at a distance of 0.71 m from the center?

+a) 3.797E+01 N/C
-b) 4.177E+01 N/C
-c) 4.595E+01 N/C
-d) 5.054E+01 N/C
-e) 5.560E+01 N/C

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### Key: W0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.214E+01 N·m2/C
-b) 2.436E+01 N·m2/C
-c) 2.679E+01 N·m2/C
-d) 2.947E+01 N·m2/C
+e) 3.242E+01 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

-a) 1.114E+01 N/C
+b) 1.225E+01 N/C
-c) 1.347E+01 N/C
-d) 1.482E+01 N/C
-e) 1.630E+01 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.439E+01 N·m2/C
-b) 5.983E+01 N·m2/C
-c) 6.581E+01 N·m2/C
+d) 7.239E+01 N·m2/C
-e) 7.963E+01 N·m2/C

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#### Key: W1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 8.314E+01 N·m2/C
-b) 9.146E+01 N·m2/C
-c) 1.006E+02 N·m2/C
-d) 1.107E+02 N·m2/C
-e) 1.217E+02 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 4.7 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.2 m from the center of the shells?

+a) 9.592E+00 N/C
-b) 1.055E+01 N/C
-c) 1.161E+01 N/C
-d) 1.277E+01 N/C
-e) 1.404E+01 N/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

-a) 1.128E+04 V·m
-b) 1.241E+04 V·m
-c) 1.365E+04 V·m
+d) 1.502E+04 V·m
-e) 1.652E+04 V·m
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.2 m, z=z0=1.6 m, and z=z1=4.7 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.7m2 ,and those in the zx plane have area 4.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 43° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 2.214E+01 N·m2/C
-b) 2.436E+01 N·m2/C
-c) 2.679E+01 N·m2/C
-d) 2.947E+01 N·m2/C
+e) 3.242E+01 N·m2/C

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#### Key: W2

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.750E+01 N·m2/C
-b) 4.125E+01 N·m2/C
-c) 4.537E+01 N·m2/C
+d) 4.991E+01 N·m2/C
-e) 5.490E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=5), and (x=7, y=5), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.4}{\hat {i}}+4x^{1.7}{\hat {j}}+4y^{2.1}{\hat {k}}}$

-a) 1.206E+03 V·m
+b) 1.326E+03 V·m
-c) 1.459E+03 V·m
-d) 1.605E+03 V·m
-e) 1.765E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.5 m, z=z0=1.7 m, and z=z1=5.1 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 9.9m2 ,and those in the zx plane have area 7.8m2. An electric field of magnitude 6 N/C has components in the y and z directions and is directed at 58° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.698E+01 N·m2/C
-b) 1.868E+01 N·m2/C
-c) 2.055E+01 N·m2/C
-d) 2.260E+01 N·m2/C
+e) 2.486E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 6.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.1 m from the center of the shells?

-a) 3.251E+01 N/C
-b) 3.577E+01 N/C
-c) 3.934E+01 N/C
-d) 4.328E+01 N/C
+e) 4.760E+01 N/C

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### Key: X0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.6 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=5.9 m, z=z0=1.9 m, and z=z1=5.0 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 12.0m2 ,and those in the zx plane have area 8.1m2. An electric field has the xyz components (0, 8.1, 6.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 6.529E+01 N·m2/C
-b) 7.181E+01 N·m2/C
-c) 7.900E+01 N·m2/C
-d) 8.690E+01 N·m2/C
-e) 9.559E+01 N·m2/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=6, y=0), (x=0, y=3), and (x=6, y=3), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{1.6}{\hat {i}}+3x^{2.6}{\hat {j}}+2y^{3.2}{\hat {k}}}$

-a) 1.969E+02 V·m
-b) 2.166E+02 V·m
-c) 2.383E+02 V·m
-d) 2.621E+02 V·m
+e) 2.883E+02 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.439E+01 N·m2/C
-b) 5.983E+01 N·m2/C
-c) 6.581E+01 N·m2/C
+d) 7.239E+01 N·m2/C
-e) 7.963E+01 N·m2/C

4) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

-a) 2.988E+00 N/C
-b) 3.287E+00 N/C
-c) 3.616E+00 N/C
-d) 3.977E+00 N/C
+e) 4.375E+00 N/C

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#### Key: X1

1) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=4), and (x=7, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=2y^{2.2}{\hat {i}}+3x^{2.1}{\hat {j}}+5y^{3.3}{\hat {k}}}$

-a) 2.610E+03 V·m
-b) 2.871E+03 V·m
+c) 3.158E+03 V·m
-d) 3.474E+03 V·m
-e) 3.822E+03 V·m
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.4 m, z=z0=1.5 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 4.6m2 ,and those in the zx plane have area 6.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.222E+01 N·m2/C
-b) 3.544E+01 N·m2/C
-c) 3.899E+01 N·m2/C
-d) 4.289E+01 N·m2/C
-e) 4.718E+01 N·m2/C

3) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

-a) 1.114E+01 N/C
+b) 1.225E+01 N/C
-c) 1.347E+01 N/C
-d) 1.482E+01 N/C
-e) 1.630E+01 N/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.614E+01 N·m2/C
+b) 7.275E+01 N·m2/C
-c) 8.003E+01 N·m2/C
-d) 8.803E+01 N·m2/C
-e) 9.683E+01 N·m2/C

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#### Key: X2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.8 m from the center of the shells?

-a) 2.988E+00 N/C
-b) 3.287E+00 N/C
-c) 3.616E+00 N/C
-d) 3.977E+00 N/C
+e) 4.375E+00 N/C

2) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=8, y=0), (x=0, y=8), and (x=8, y=8), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=1y^{2.8}{\hat {i}}+5x^{2.7}{\hat {j}}+5y^{1.6}{\hat {k}}}$

+a) 3.429E+03 V·m
-b) 3.771E+03 V·m
-c) 4.149E+03 V·m
-d) 4.564E+03 V·m
-e) 5.020E+03 V·m
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.6 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=5.6 m. The surfaces in the yz plane each have area 16.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 5.6m2. An electric field has the xyz components (0, 5.5, 9.1) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.074E+01 N·m2/C
-b) 3.382E+01 N·m2/C
-c) 3.720E+01 N·m2/C
-d) 4.092E+01 N·m2/C
-e) 4.501E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.4 m. The other four surfaces are rectangles in y=y0=1.9 m, y=y1=5.3 m, z=z0=1.4 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 8.2m2 ,and those in the zx plane have area 9.8m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 58° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.270E+01 N·m2/C
-b) 6.897E+01 N·m2/C
-c) 7.586E+01 N·m2/C
-d) 8.345E+01 N·m2/C
+e) 9.179E+01 N·m2/C

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### Key: Y0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.8 m, z=z0=1.7 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 8.5m2 ,and those in the zx plane have area 7.2m2. An electric field of magnitude 14 N/C has components in the y and z directions and is directed at 55° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 8.314E+01 N·m2/C
-b) 9.146E+01 N·m2/C
-c) 1.006E+02 N·m2/C
-d) 1.107E+02 N·m2/C
-e) 1.217E+02 N·m2/C

2) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.2 nano-Coulombs. What is the magnitude of the electric field at a distance of 4.6 m from the center of the shells?

-a) 1.114E+01 N/C
+b) 1.225E+01 N/C
-c) 1.347E+01 N/C
-d) 1.482E+01 N/C
-e) 1.630E+01 N/C

3) A non-conducting sphere of radius R=3.0 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.2 (r≤R) where a=2 nC·m-1.8. What is the magnitude of the electric field at a distance of 2.1 m from the center?

-a) 2.274E+02 N/C
-b) 2.501E+02 N/C
+c) 2.751E+02 N/C
-d) 3.026E+02 N/C
-e) 3.329E+02 N/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=7, y=0), (x=0, y=7), and (x=7, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.3}{\hat {i}}+3x^{2.4}{\hat {j}}+2y^{1.8}{\hat {k}}}$

-a) 8.731E+02 V·m
-b) 9.604E+02 V·m
-c) 1.056E+03 V·m
+d) 1.162E+03 V·m
-e) 1.278E+03 V·m

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#### Key: Y1

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.4 nano-Coulombs. What is the magnitude of the electric field at a distance of 5.4 m from the center of the shells?

-a) 8.580E+00 N/C
-b) 9.438E+00 N/C
-c) 1.038E+01 N/C
+d) 1.142E+01 N/C
-e) 1.256E+01 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=5.3 m, z=z0=1.2 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 7.7m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.989E+01 N·m2/C
-b) 6.588E+01 N·m2/C
-c) 7.247E+01 N·m2/C
+d) 7.971E+01 N·m2/C
-e) 8.769E+01 N·m2/C

3) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=4), and (x=4, y=4), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=4y^{2.2}{\hat {i}}+1x^{3.0}{\hat {j}}+2y^{1.7}{\hat {k}}}$

-a) 8.545E+01 V·m
-b) 9.400E+01 V·m
-c) 1.034E+02 V·m
-d) 1.137E+02 V·m
+e) 1.251E+02 V·m

4) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

+a) 2.079E+02 N/C
-b) 2.287E+02 N/C
-c) 2.516E+02 N/C
-d) 2.767E+02 N/C
-e) 3.044E+02 N/C

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#### Key: Y2

1) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 1.3 m from the center of the shells?

-a) 2.837E+01 N/C
-b) 3.121E+01 N/C
-c) 3.433E+01 N/C
-d) 3.776E+01 N/C
+e) 4.154E+01 N/C

2) A non-conducting sphere of radius R=3.7 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 6.411E+02 N/C
-b) 7.052E+02 N/C
+c) 7.757E+02 N/C
-d) 8.533E+02 N/C
-e) 9.386E+02 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.6 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.4 m, z=z0=1.5 m, and z=z1=5.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 4.6m2 ,and those in the zx plane have area 6.4m2. An electric field of magnitude 8 N/C has components in the y and z directions and is directed at 39° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
+a) 3.222E+01 N·m2/C
-b) 3.544E+01 N·m2/C
-c) 3.899E+01 N·m2/C
-d) 4.289E+01 N·m2/C
-e) 4.718E+01 N·m2/C

4) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=5, y=0), (x=0, y=7), and (x=5, y=7), where x and y are measured in meters. The electric field is,
${\displaystyle {\vec {E}}=3y^{2.7}{\hat {i}}+1x^{2.5}{\hat {j}}+3y^{3.3}{\hat {k}}}$

-a) 1.128E+04 V·m
-b) 1.241E+04 V·m
-c) 1.365E+04 V·m
+d) 1.502E+04 V·m
-e) 1.652E+04 V·m

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### Key: Z0

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=4.6 m, z=z0=1.6 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 13.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 9.7m2. An electric field of magnitude 17 N/C has components in the y and z directions and is directed at 43° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 8.415E+01 N·m2/C
-b) 9.256E+01 N·m2/C
-c) 1.018E+02 N·m2/C
+d) 1.120E+02 N·m2/C
-e) 1.232E+02 N·m2/C

2) A non-conducting sphere of radius R=3.8 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.7 (r≤R) where a=3 nC·m-1.3. What is the magnitude of the electric field at a distance of 3.1 m from the center?

-a) 1.390E+03 N/C
+b) 1.530E+03 N/C
-c) 1.682E+03 N/C
-d) 1.851E+03 N/C
-e) 2.036E+03 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.920E+01 N·m2/C
-b) 7.612E+01 N·m2/C
-c) 8.373E+01 N·m2/C
+d) 9.210E+01 N·m2/C
-e) 1.013E+02 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.0 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.2 m, z=z0=1.3 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.8m2 ,and those in the zx plane have area 9.0m2. An electric field has the xyz components (0, 6.1, 5.6) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 4.125E+01 N·m2/C
-b) 4.537E+01 N·m2/C
-c) 4.991E+01 N·m2/C
+d) 5.490E+01 N·m2/C
-e) 6.039E+01 N·m2/C

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#### Key: Z1

1) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.7 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.7 m, z=z0=1.4 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 14.0m2. Those in the xy plane have area 7.1m2 ,and those in the zx plane have area 5.8m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 33° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.920E+01 N·m2/C
-b) 7.612E+01 N·m2/C
-c) 8.373E+01 N·m2/C
+d) 9.210E+01 N·m2/C
-e) 1.013E+02 N·m2/C

2) A non-conducting sphere of radius R=2.5 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.8 (r≤R) where a=2 nC·m-1.2. What is the magnitude of the electric field at a distance of 1.7 m from the center?

+a) 2.079E+02 N/C
-b) 2.287E+02 N/C
-c) 2.516E+02 N/C
-d) 2.767E+02 N/C
-e) 3.044E+02 N/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.3 m, z=z0=1.3 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 10.0m2 ,and those in the zx plane have area 7.5m2. An electric field has the xyz components (0, 9.7, 9.3) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 6.614E+01 N·m2/C
+b) 7.275E+01 N·m2/C
-c) 8.003E+01 N·m2/C
-d) 8.803E+01 N·m2/C
-e) 9.683E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.9 m, z=z0=1.1 m, and z=z1=5.3 m. The surfaces in the yz plane each have area 15.0m2. Those in the xy plane have area 8.8m2 ,and those in the zx plane have area 10.0m2. An electric field of magnitude 9 N/C has components in the y and z directions and is directed at 50° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 5.439E+01 N·m2/C
-b) 5.983E+01 N·m2/C
-c) 6.581E+01 N·m2/C
+d) 7.239E+01 N·m2/C
-e) 7.963E+01 N·m2/C

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#### Key: Z2

1) A non-conducting sphere of radius R=3.9 m has a non-uniform charge density that varies with the distnce from its center as given by ρ(r)=ar1.4 (r≤R) where a=2 nC·m-1.6. What is the magnitude of the electric field at a distance of 2.6 m from the center?

-a) 3.821E+02 N/C
-b) 4.203E+02 N/C
-c) 4.624E+02 N/C
+d) 5.086E+02 N/C
-e) 5.594E+02 N/C
2) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.8 m, z=z0=1.7 m, and z=z1=5.8 m. The surfaces in the yz plane each have area 18.0m2. Those in the xy plane have area 5.6m2 ,and those in the zx plane have area 5.3m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 40° above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.712E+01 N·m2/C
-b) 4.083E+01 N·m2/C
+c) 4.491E+01 N·m2/C
-d) 4.940E+01 N·m2/C
-e) 5.434E+01 N·m2/C
3) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.5 m. The other four surfaces are rectangles in y=y0=1.4 m, y=y1=4.3 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 9.9m2. Those in the xy plane have area 4.3m2 ,and those in the zx plane have area 5.1m2. An electric field of magnitude 19 N/C has components in the y and z directions and is directed at 31° from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 3.750E+01 N·m2/C
-b) 4.125E+01 N·m2/C
-c) 4.537E+01 N·m2/C
+d) 4.991E+01 N·m2/C
-e) 5.490E+01 N·m2/C
4) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.4 m. The other four surfaces are rectangles in y=y0=1.3 m, y=y1=5.6 m, z=z0=1.7 m, and z=z1=4.5 m. The surfaces in the yz plane each have area 12.0m2. Those in the xy plane have area 6.0m2 ,and those in the zx plane have area 3.9m2. An electric field has the xyz components (0, 6.5, 9.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
-a) 1.740E+01 N·m2/C
-b) 1.914E+01 N·m2/C
-c) 2.106E+01 N·m2/C
-d) 2.316E+01 N·m2/C
+e) 2.548E+01 N·m2/C

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