The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.

  • Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
  • At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
    • Quizbank physics 1 (id 60675)
    • Quizbank physics 2 (id 61712)
    • Quizbank astronomy (id 63705)


See special:permalink/1894335 for a wikitext version of this quiz.

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\newif\ifkey %estabkishes Boolean ifkey to turn on and off endnotes

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\begin{document}
\title{d\_cp2.6}
\author{The LaTex code that creates this quiz is released to the Public Domain\\
Attribution for each question is documented in the Appendix}
\maketitle
\begin{center}                                                                                
 \includegraphics[width=0.15\textwidth]{666px-Wikiversity-logo-en.png}
\\Latex markup at\\
\footnotesize{ \url{https://en.wikiversity.org/wiki/special:permalink/1894335}}
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\begin{multicols}{3}
\tableofcontents
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\pagebreak\section{Quiz}
\keytrue
\printanswers
\begin{questions}
\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1\,m, y=y\textsubscript{1}=5\,m, z=z\textsubscript{0}=1\,m, and z=z\textsubscript{1}=3\,m. The surfaces in the yz plane each have area 8m\textsuperscript{2}. Those in the xy plane have area 12m\textsuperscript{2} ,and those in the zx plane have area 6m\textsuperscript{2}. An electric field of magnitude 10\,N/C has components in the y and z directions and is directed at 30\(^\circ\) 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?\ifkey\endnote{Example 6.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7Rx6Svvy@4/61-Electric-Flux\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 3.549E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 3.904E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 4.294E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 4.724E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \CorrectChoice 5.196E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices}

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1\,m, y=y\textsubscript{1}=5\,m, z=z\textsubscript{0}=1\,m, and z=z\textsubscript{1}=3\,m. The surfaces in the yz plane each have area 8m\textsuperscript{2}. Those in the xy plane have area 12m\textsuperscript{2} ,and those in the zx plane have area 6m\textsuperscript{2}. An electric field of magnitude 10\,N/C has components in the y and z directions and is directed at 60\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?\ifkey\endnote{Example 6.3a from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7Rx6Svvy@4/61-Electric-Flux\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 4.724E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \CorrectChoice 5.196E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 5.716E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 6.287E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 6.916E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices}

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1\,m, y=y\textsubscript{1}=5\,m, z=z\textsubscript{0}=1\,m, and z=z\textsubscript{1}=3\,m. The surfaces in the yz plane each have area 8m\textsuperscript{2}. Those in the xy plane have area 12m\textsuperscript{2} ,and those in the zx plane have area 6m\textsuperscript{2}. An electric field has the xyz components (0,\,8.7,\,5.0)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?\ifkey\endnote{Example 6.3b from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7Rx6Svvy@4/61-Electric-Flux\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 4.745E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \CorrectChoice 5.220E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 5.742E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 6.316E+01\,N\(\cdot\) m\textsuperscript{2}/C
  \choice 6.948E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices}

\question 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=3,\,y=0), (x=0,\,y=2), and (x=3,\,y=2), where x and y are measured in meters. The electric field is, \(\vec E=1y^{1}\hat i +2x^{3}\hat j +3y^{2}\hat k\). \ifkey\endnote{Example 6.4 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7Rx6Svvy@4/61-Electric-Flux\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 1.983E+01\,V\(\cdot\) m
  \choice 2.182E+01\,V\(\cdot\) m
  \CorrectChoice 2.400E+01\,V\(\cdot\) m
  \choice 2.640E+01\,V\(\cdot\) m
  \choice 2.904E+01\,V\(\cdot\) m
\end{choices}

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 5\,nano-Coulombs. What is the magnitude of the electric field at a distance of 3.5\,m from the center of the shells?\ifkey\endnote{Inspired by Example 6.6 from OpenStax University Physics2, but modified by [[user:Guy vandegrift]] to be Public Domain (CC0)\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \CorrectChoice 1.102E+01\,N/C
  \choice 1.212E+01\,N/C
  \choice 1.333E+01\,N/C
  \choice 1.467E+01\,N/C
  \choice 1.613E+01\,N/C
\end{choices}

\question A non-conducting sphere of radius R=2\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{2} (r\(x\)R) where a=1\,nC\(\cdot\) m\textsuperscript{-1}. What is the magnitude of the electric field at a distance of 1\,m from the center? \ifkey\endnote{Example 6.7 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:7NEpGtkt@4/63-Applying-Gausss-Law\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1894335}}}\fi
 \begin{choices}
  \choice 1.867E+01\,N/C
  \choice 2.053E+01\,N/C
  \CorrectChoice 2.259E+01\,N/C
  \choice 2.485E+01\,N/C
  \choice 2.733E+01\,N/C
\end{choices}

\end{questions}
\newpage
\section{Renditions}  %%% Renditions %%%%

\subsection{}%%%% subsection 1

\begin{questions} %%%%%%% begin questions

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.6\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 9.0m\textsuperscript{2} ,and those in the zx plane have area 9.5m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 35\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  6.445E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.089E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.798E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 8.578E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.436E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=5.9\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 3.6m\textsuperscript{2} ,and those in the zx plane have area 6.7m\textsuperscript{2}. An electric field of magnitude 16\,N/C has components in the y and z directions and is directed at 53\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  4.420E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.862E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.348E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.882E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 6.471E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.1\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.0\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=5.7\,m. The surfaces in the yz plane each have area 14.0m\textsuperscript{2}. Those in the xy plane have area 3.9m\textsuperscript{2} ,and those in the zx plane have area 4.3m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 31\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  4.521E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.973E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.470E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.017E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 6.619E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.9\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=5.1\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.7\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 6.6m\textsuperscript{2} ,and those in the zx plane have area 6.5m\textsuperscript{2}. An electric field of magnitude 12\,N/C has components in the y and z directions and is directed at 46\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 5.385E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.923E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.516E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.167E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.884E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=5.2\,m, z=z\textsubscript{0}=1.6\,m, and z=z\textsubscript{1}=4.7\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 4.7m\textsuperscript{2} ,and those in the zx plane have area 4.0m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 43\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  2.214E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.436E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.679E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.947E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 3.242E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.1\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.2\,m. The surfaces in the yz plane each have area 9.4m\textsuperscript{2}. Those in the xy plane have area 8.2m\textsuperscript{2} ,and those in the zx plane have area 5.0m\textsuperscript{2}. An electric field of magnitude 6\,N/C has components in the y and z directions and is directed at 29\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  2.186E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.404E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.645E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.909E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.200E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 14.0m\textsuperscript{2}. Those in the xy plane have area 11.0m\textsuperscript{2} ,and those in the zx plane have area 8.3m\textsuperscript{2}. An electric field of magnitude 9\,N/C has components in the y and z directions and is directed at 39\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  4.809E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.290E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.819E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.401E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.041E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.1\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=4.3\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 8.8m\textsuperscript{2} ,and those in the zx plane have area 6.7m\textsuperscript{2}. An electric field of magnitude 10\,N/C has components in the y and z directions and is directed at 39\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  3.924E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.316E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.748E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.222E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.745E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.1\,m. The surfaces in the yz plane each have area 8.7m\textsuperscript{2}. Those in the xy plane have area 7.2m\textsuperscript{2} ,and those in the zx plane have area 7.0m\textsuperscript{2}. An electric field of magnitude 12\,N/C has components in the y and z directions and is directed at 58\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  4.024E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.426E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.868E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.355E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.891E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 9.8m\textsuperscript{2} ,and those in the zx plane have area 7.4m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 46\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  8.457E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 9.303E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.023E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.126E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.238E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.7\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=4.8\,m. The surfaces in the yz plane each have area 14.0m\textsuperscript{2}. Those in the xy plane have area 7.1m\textsuperscript{2} ,and those in the zx plane have area 5.8m\textsuperscript{2}. An electric field of magnitude 19\,N/C has components in the y and z directions and is directed at 33\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  6.920E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.612E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.373E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 9.210E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.013E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.9\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=5.7\,m. The surfaces in the yz plane each have area 9.6m\textsuperscript{2}. Those in the xy plane have area 4.1m\textsuperscript{2} ,and those in the zx plane have area 6.8m\textsuperscript{2}. An electric field of magnitude 13\,N/C has components in the y and z directions and is directed at 27\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 7.876E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.664E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.531E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.048E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.153E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.9\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 5.3m\textsuperscript{2} ,and those in the zx plane have area 5.0m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 29\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 7.793E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.572E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.429E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.037E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.141E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=5.2\,m. The surfaces in the yz plane each have area 18.0m\textsuperscript{2}. Those in the xy plane have area 12.0m\textsuperscript{2} ,and those in the zx plane have area 11.0m\textsuperscript{2}. An electric field of magnitude 13\,N/C has components in the y and z directions and is directed at 60\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  5.606E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.167E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.784E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.462E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.208E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=5.0\,m. The surfaces in the yz plane each have area 17.0m\textsuperscript{2}. Those in the xy plane have area 6.4m\textsuperscript{2} ,and those in the zx plane have area 5.3m\textsuperscript{2}. An electric field of magnitude 5\,N/C has components in the y and z directions and is directed at 25\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.992E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.192E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.411E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.652E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.917E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.5\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=5.1\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 9.9m\textsuperscript{2} ,and those in the zx plane have area 7.8m\textsuperscript{2}. An electric field of magnitude 6\,N/C has components in the y and z directions and is directed at 58\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.698E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.868E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.055E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.260E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.486E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=5.8\,m. The surfaces in the yz plane each have area 18.0m\textsuperscript{2}. Those in the xy plane have area 5.6m\textsuperscript{2} ,and those in the zx plane have area 5.3m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 40\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  3.712E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.083E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.491E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.940E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.434E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.0\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.2\,m. The surfaces in the yz plane each have area 9.0m\textsuperscript{2}. Those in the xy plane have area 6.2m\textsuperscript{2} ,and those in the zx plane have area 5.8m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 32\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  3.695E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.065E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.472E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.919E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.411E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=4.9\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.6\,m. The surfaces in the yz plane each have area 16.0m\textsuperscript{2}. Those in the xy plane have area 6.8m\textsuperscript{2} ,and those in the zx plane have area 7.7m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 57\(^\circ\) 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?
\begin{choices} %%%%%%% begin choices
    \choice  6.898E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.588E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.347E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.181E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.010E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 2

\begin{questions} %%%%%%% begin questions

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.8\,m, y=y\textsubscript{1}=4.8\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.3\,m. The surfaces in the yz plane each have area 7.5m\textsuperscript{2}. Those in the xy plane have area 3.6m\textsuperscript{2} ,and those in the zx plane have area 3.0m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 49\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.058E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.264E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.491E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.740E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.014E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.9\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.9\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.3\,m. The surfaces in the yz plane each have area 17.0m\textsuperscript{2}. Those in the xy plane have area 12.0m\textsuperscript{2} ,and those in the zx plane have area 12.0m\textsuperscript{2}. An electric field of magnitude 5\,N/C has components in the y and z directions and is directed at 26\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  1.737E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.910E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.101E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.311E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.543E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.4\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=5.6\,m. The surfaces in the yz plane each have area 16.0m\textsuperscript{2}. Those in the xy plane have area 9.6m\textsuperscript{2} ,and those in the zx plane have area 11.0m\textsuperscript{2}. An electric field of magnitude 15\,N/C has components in the y and z directions and is directed at 33\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 8.921E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.813E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.079E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.187E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.306E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=4.6\,m, z=z\textsubscript{0}=1.6\,m, and z=z\textsubscript{1}=5.8\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 7.1m\textsuperscript{2} ,and those in the zx plane have area 9.7m\textsuperscript{2}. An electric field of magnitude 17\,N/C has components in the y and z directions and is directed at 43\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  8.415E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.256E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.018E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 1.120E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.232E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.0\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.8\,m, y=y\textsubscript{1}=5.8\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=5.9\,m. The surfaces in the yz plane each have area 16.0m\textsuperscript{2}. Those in the xy plane have area 8.0m\textsuperscript{2} ,and those in the zx plane have area 8.0m\textsuperscript{2}. An electric field of magnitude 8\,N/C has components in the y and z directions and is directed at 39\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.662E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.028E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.430E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.873E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.361E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=5.9\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 7.6m\textsuperscript{2} ,and those in the zx plane have area 13.0m\textsuperscript{2}. An electric field of magnitude 8\,N/C has components in the y and z directions and is directed at 46\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.988E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.487E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.035E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.639E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.303E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.7\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.7\,m. The surfaces in the yz plane each have area 9.6m\textsuperscript{2}. Those in the xy plane have area 9.2m\textsuperscript{2} ,and those in the zx plane have area 8.1m\textsuperscript{2}. An electric field of magnitude 6\,N/C has components in the y and z directions and is directed at 32\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.134E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.347E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.582E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.840E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.124E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.5\,m, and z=z\textsubscript{1}=4.7\,m. The surfaces in the yz plane each have area 8.3m\textsuperscript{2}. Those in the xy plane have area 5.7m\textsuperscript{2} ,and those in the zx plane have area 7.0m\textsuperscript{2}. An electric field of magnitude 18\,N/C has components in the y and z directions and is directed at 28\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  5.408E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.949E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.544E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.198E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.918E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.5\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 4.6m\textsuperscript{2} ,and those in the zx plane have area 6.4m\textsuperscript{2}. An electric field of magnitude 8\,N/C has components in the y and z directions and is directed at 39\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.222E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.544E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.899E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.289E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.718E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.8\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 7.7m\textsuperscript{2} ,and those in the zx plane have area 9.5m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 50\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  5.989E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.588E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.247E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.971E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.769E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.6\,m. The surfaces in the yz plane each have area 9.9m\textsuperscript{2}. Those in the xy plane have area 4.3m\textsuperscript{2} ,and those in the zx plane have area 5.1m\textsuperscript{2}. An electric field of magnitude 19\,N/C has components in the y and z directions and is directed at 31\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.750E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.125E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.537E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.991E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.490E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.8\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=4.6\,m. The surfaces in the yz plane each have area 9.9m\textsuperscript{2}. Those in the xy plane have area 8.5m\textsuperscript{2} ,and those in the zx plane have area 7.2m\textsuperscript{2}. An electric field of magnitude 14\,N/C has components in the y and z directions and is directed at 55\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 8.314E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.146E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.006E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.107E+02\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.217E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=5.7\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.5\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 6.0m\textsuperscript{2} ,and those in the zx plane have area 3.5m\textsuperscript{2}. An electric field of magnitude 5\,N/C has components in the y and z directions and is directed at 38\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  9.823E+00\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 1.080E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.189E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.307E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.438E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.9\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=5.3\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 8.8m\textsuperscript{2} ,and those in the zx plane have area 10.0m\textsuperscript{2}. An electric field of magnitude 9\,N/C has components in the y and z directions and is directed at 50\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  5.439E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.983E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.581E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.239E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.963E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=4.4\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 13.0m\textsuperscript{2}. Those in the xy plane have area 5.0m\textsuperscript{2} ,and those in the zx plane have area 6.6m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 34\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.756E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.032E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.335E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.668E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.035E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.9\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 14.0m\textsuperscript{2}. Those in the xy plane have area 8.2m\textsuperscript{2} ,and those in the zx plane have area 9.8m\textsuperscript{2}. An electric field of magnitude 11\,N/C has components in the y and z directions and is directed at 58\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  6.270E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.897E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.586E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.345E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 9.179E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.6\,m, z=z\textsubscript{0}=1.4\,m, and z=z\textsubscript{1}=4.5\,m. The surfaces in the yz plane each have area 9.0m\textsuperscript{2}. Those in the xy plane have area 6.4m\textsuperscript{2} ,and those in the zx plane have area 6.8m\textsuperscript{2}. An electric field of magnitude 15\,N/C has components in the y and z directions and is directed at 31\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  3.959E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.354E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.790E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.269E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.796E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.9\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.2\,m. The surfaces in the yz plane each have area 18.0m\textsuperscript{2}. Those in the xy plane have area 8.5m\textsuperscript{2} ,and those in the zx plane have area 7.0m\textsuperscript{2}. An electric field of magnitude 12\,N/C has components in the y and z directions and is directed at 49\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  4.777E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.254E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.780E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 6.358E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.993E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=5.7\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=5.4\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 11.0m\textsuperscript{2} ,and those in the zx plane have area 8.4m\textsuperscript{2}. An electric field of magnitude 8\,N/C has components in the y and z directions and is directed at 26\(^\circ\) from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.012E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.213E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.435E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.678E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.946E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 3

\begin{questions} %%%%%%% begin questions

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.0\,m, z=z\textsubscript{0}=1.6\,m, and z=z\textsubscript{1}=4.8\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 4.5m\textsuperscript{2} ,and those in the zx plane have area 4.2m\textsuperscript{2}. An electric field has the xyz components (0,\,6.4,\,6.8)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 2.662E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.929E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.222E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.544E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.898E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.9\,m. The surfaces in the yz plane each have area 8.1m\textsuperscript{2}. Those in the xy plane have area 7.0m\textsuperscript{2} ,and those in the zx plane have area 8.4m\textsuperscript{2}. An electric field has the xyz components (0,\,9.2,\,7.1)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  6.364E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.000E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.700E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.470E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.317E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.2\,m, y=y\textsubscript{1}=5.9\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=5.0\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 12.0m\textsuperscript{2} ,and those in the zx plane have area 8.1m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 6.529E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.181E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.900E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.690E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.559E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.6\,m. The surfaces in the yz plane each have area 16.0m\textsuperscript{2}. Those in the xy plane have area 4.8m\textsuperscript{2} ,and those in the zx plane have area 5.6m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.074E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.382E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.720E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.092E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.501E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.3\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.2\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 9.6m\textsuperscript{2}. Those in the xy plane have area 8.5m\textsuperscript{2} ,and those in the zx plane have area 6.0m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  4.730E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.203E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.723E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.295E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.925E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 10.0m\textsuperscript{2}. Those in the xy plane have area 8.1m\textsuperscript{2} ,and those in the zx plane have area 10.0m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  7.081E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.789E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 8.568E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.425E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.037E+02\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=5.0\,m, z=z\textsubscript{0}=1.6\,m, and z=z\textsubscript{1}=5.9\,m. The surfaces in the yz plane each have area 15.0m\textsuperscript{2}. Those in the xy plane have area 6.5m\textsuperscript{2} ,and those in the zx plane have area 7.7m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 6.192E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.811E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.492E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.242E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.066E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.2\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=5.0\,m, z=z\textsubscript{0}=1.9\,m, and z=z\textsubscript{1}=4.3\,m. The surfaces in the yz plane each have area 7.9m\textsuperscript{2}. Those in the xy plane have area 4.0m\textsuperscript{2} ,and those in the zx plane have area 2.9m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.388E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 1.526E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.679E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.847E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.032E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.7\,m, and z=z\textsubscript{1}=4.5\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 6.0m\textsuperscript{2} ,and those in the zx plane have area 3.9m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.740E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  1.914E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.106E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.316E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.548E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.0\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.4\,m, y=y\textsubscript{1}=4.7\,m, z=z\textsubscript{0}=1.2\,m, and z=z\textsubscript{1}=4.1\,m. The surfaces in the yz plane each have area 9.6m\textsuperscript{2}. Those in the xy plane have area 6.6m\textsuperscript{2} ,and those in the zx plane have area 5.8m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  3.328E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.660E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.026E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.429E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.872E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.0\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.8\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.8\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 4.8m\textsuperscript{2} ,and those in the zx plane have area 9.0m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  4.125E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.537E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.991E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 5.490E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.039E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.4\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=4.8\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.8\,m. The surfaces in the yz plane each have area 11.0m\textsuperscript{2}. Those in the xy plane have area 8.9m\textsuperscript{2} ,and those in the zx plane have area 7.2m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  2.901E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.192E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.511E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.862E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 4.248E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.6\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=4.4\,m. The surfaces in the yz plane each have area 10.0m\textsuperscript{2}. Those in the xy plane have area 6.4m\textsuperscript{2} ,and those in the zx plane have area 4.2m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.891E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.080E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.288E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.517E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.768E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.1\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.2\,m, z=z\textsubscript{0}=1.1\,m, and z=z\textsubscript{1}=4.5\,m. The surfaces in the yz plane each have area 8.5m\textsuperscript{2}. Those in the xy plane have area 2.8m\textsuperscript{2} ,and those in the zx plane have area 3.7m\textsuperscript{2}. An electric field has the xyz components (0,\,7.4,\,8.9)\,N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
\begin{choices} %%%%%%% begin choices
    \choice  2.079E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.287E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  2.516E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 2.768E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.044E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.3\,m, y=y\textsubscript{1}=5.3\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.3\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 10.0m\textsuperscript{2} ,and those in the zx plane have area 7.5m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  6.614E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.275E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.003E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.803E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  9.683E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.1\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.8\,m, and z=z\textsubscript{1}=5.5\,m. The surfaces in the yz plane each have area 17.0m\textsuperscript{2}. Those in the xy plane have area 13.0m\textsuperscript{2} ,and those in the zx plane have area 10.0m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  4.953E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.449E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.993E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.593E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 7.252E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.7\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.5\,m, y=y\textsubscript{1}=5.6\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=4.2\,m. The surfaces in the yz plane each have area 12.0m\textsuperscript{2}. Those in the xy plane have area 11.0m\textsuperscript{2} ,and those in the zx plane have area 7.8m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \choice  5.000E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  5.500E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.050E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \CorrectChoice 6.656E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.321E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=1.5\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.6\,m, y=y\textsubscript{1}=4.3\,m, z=z\textsubscript{0}=1.3\,m, and z=z\textsubscript{1}=5.1\,m. The surfaces in the yz plane each have area 10.0m\textsuperscript{2}. Those in the xy plane have area 4.0m\textsuperscript{2} ,and those in the zx plane have area 5.7m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.249E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.574E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  3.931E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.324E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  4.757E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices

\question 
    \includegraphics[width=0.12\textwidth]{Boxin2Dxyzaligned.png}Each surface of the rectangular box shown is aligned with the xyz coordinate system.  Two surfaces occupy identical rectangles in the planes x=0 and x=x\textsubscript{1}=2.8\,m. The other four surfaces are rectangles in y=y\textsubscript{0}=1.7\,m, y=y\textsubscript{1}=4.5\,m, z=z\textsubscript{0}=1.5\,m, and z=z\textsubscript{1}=5.0\,m. The surfaces in the yz plane each have area 9.8m\textsuperscript{2}. Those in the xy plane have area 7.8m\textsuperscript{2} ,and those in the zx plane have area 9.8m\textsuperscript{2}. 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 5.978E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  6.576E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.233E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  7.957E+01\,N\(\cdot\) m\textsuperscript{2}/C
    \choice  8.752E+01\,N\(\cdot\) m\textsuperscript{2}/C
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 4

\begin{questions} %%%%%%% begin questions

\question 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=6), and (x=4,\,y=6), where x and y are measured in meters. The electric field is, \(\vec E=3y^{1.9}\hat i +3x^{1.5}\hat j +3y^{1.6}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  3.658E+02\,V\(\cdot\) m
    \choice  4.024E+02\,V\(\cdot\) m
    \choice  4.426E+02\,V\(\cdot\) m
    \CorrectChoice 4.869E+02\,V\(\cdot\) m
    \choice  5.355E+02\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=4y^{2.2}\hat i +1x^{3.0}\hat j +2y^{1.7}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  8.545E+01\,V\(\cdot\) m
    \choice  9.400E+01\,V\(\cdot\) m
    \choice  1.034E+02\,V\(\cdot\) m
    \choice  1.137E+02\,V\(\cdot\) m
    \CorrectChoice 1.251E+02\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=4y^{2.3}\hat i +3x^{2.4}\hat j +2y^{1.8}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  8.731E+02\,V\(\cdot\) m
    \choice  9.604E+02\,V\(\cdot\) m
    \choice  1.056E+03\,V\(\cdot\) m
    \CorrectChoice 1.162E+03\,V\(\cdot\) m
    \choice  1.278E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=3y^{2.7}\hat i +1x^{2.5}\hat j +3y^{3.3}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  1.128E+04\,V\(\cdot\) m
    \choice  1.241E+04\,V\(\cdot\) m
    \choice  1.365E+04\,V\(\cdot\) m
    \CorrectChoice 1.502E+04\,V\(\cdot\) m
    \choice  1.652E+04\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=3y^{2.9}\hat i +3x^{1.6}\hat j +4y^{2.5}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  4.286E+03\,V\(\cdot\) m
    \choice  4.714E+03\,V\(\cdot\) m
    \CorrectChoice 5.186E+03\,V\(\cdot\) m
    \choice  5.704E+03\,V\(\cdot\) m
    \choice  6.275E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=1y^{2.8}\hat i +5x^{2.7}\hat j +5y^{1.6}\hat k\).
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.429E+03\,V\(\cdot\) m
    \choice  3.771E+03\,V\(\cdot\) m
    \choice  4.149E+03\,V\(\cdot\) m
    \choice  4.564E+03\,V\(\cdot\) m
    \choice  5.020E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=1y^{2.4}\hat i +4x^{1.7}\hat j +4y^{2.1}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  1.206E+03\,V\(\cdot\) m
    \CorrectChoice 1.326E+03\,V\(\cdot\) m
    \choice  1.459E+03\,V\(\cdot\) m
    \choice  1.605E+03\,V\(\cdot\) m
    \choice  1.765E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=2y^{2.5}\hat i +3x^{1.8}\hat j +2y^{2.8}\hat k\).
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.337E+03\,V\(\cdot\) m
    \choice  3.670E+03\,V\(\cdot\) m
    \choice  4.037E+03\,V\(\cdot\) m
    \choice  4.441E+03\,V\(\cdot\) m
    \choice  4.885E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=3y^{2.8}\hat i +1x^{2.3}\hat j +2y^{2.9}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  2.210E+04\,V\(\cdot\) m
    \CorrectChoice 2.431E+04\,V\(\cdot\) m
    \choice  2.674E+04\,V\(\cdot\) m
    \choice  2.941E+04\,V\(\cdot\) m
    \choice  3.235E+04\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=2y^{2.2}\hat i +3x^{2.1}\hat j +5y^{3.3}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  2.610E+03\,V\(\cdot\) m
    \choice  2.871E+03\,V\(\cdot\) m
    \CorrectChoice 3.158E+03\,V\(\cdot\) m
    \choice  3.474E+03\,V\(\cdot\) m
    \choice  3.822E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=2y^{2.8}\hat i +3x^{2.8}\hat j +2y^{2.4}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  1.997E+03\,V\(\cdot\) m
    \CorrectChoice 2.197E+03\,V\(\cdot\) m
    \choice  2.417E+03\,V\(\cdot\) m
    \choice  2.659E+03\,V\(\cdot\) m
    \choice  2.924E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=4y^{1.4}\hat i +2x^{2.3}\hat j +4y^{2.3}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  2.694E+03\,V\(\cdot\) m
    \choice  2.963E+03\,V\(\cdot\) m
    \choice  3.259E+03\,V\(\cdot\) m
    \CorrectChoice 3.585E+03\,V\(\cdot\) m
    \choice  3.944E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=3y^{1.7}\hat i +3x^{1.6}\hat j +4y^{2.7}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  2.067E+03\,V\(\cdot\) m
    \choice  2.274E+03\,V\(\cdot\) m
    \CorrectChoice 2.501E+03\,V\(\cdot\) m
    \choice  2.752E+03\,V\(\cdot\) m
    \choice  3.027E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=2y^{1.8}\hat i +3x^{1.9}\hat j +5y^{3.2}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  9.952E+03\,V\(\cdot\) m
    \choice  1.095E+04\,V\(\cdot\) m
    \choice  1.204E+04\,V\(\cdot\) m
    \CorrectChoice 1.325E+04\,V\(\cdot\) m
    \choice  1.457E+04\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=4y^{2.0}\hat i +3x^{2.0}\hat j +3y^{3.0}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  4.820E+03\,V\(\cdot\) m
    \choice  5.302E+03\,V\(\cdot\) m
    \CorrectChoice 5.832E+03\,V\(\cdot\) m
    \choice  6.415E+03\,V\(\cdot\) m
    \choice  7.057E+03\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=1y^{1.6}\hat i +3x^{2.6}\hat j +2y^{3.2}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  1.969E+02\,V\(\cdot\) m
    \choice  2.166E+02\,V\(\cdot\) m
    \choice  2.383E+02\,V\(\cdot\) m
    \choice  2.621E+02\,V\(\cdot\) m
    \CorrectChoice 2.883E+02\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=2y^{2.7}\hat i +2x^{2.9}\hat j +2y^{2.0}\hat k\).
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 7.200E+01\,V\(\cdot\) m
    \choice  7.920E+01\,V\(\cdot\) m
    \choice  8.712E+01\,V\(\cdot\) m
    \choice  9.583E+01\,V\(\cdot\) m
    \choice  1.054E+02\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=1y^{2.2}\hat i +1x^{3.3}\hat j +5y^{2.4}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  7.054E+03\,V\(\cdot\) m
    \choice  7.759E+03\,V\(\cdot\) m
    \choice  8.535E+03\,V\(\cdot\) m
    \choice  9.388E+03\,V\(\cdot\) m
    \CorrectChoice 1.033E+04\,V\(\cdot\) m
\end{choices} %%% end choices

\question 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, \(\vec E=2y^{2.0}\hat i +2x^{2.1}\hat j +3y^{2.5}\hat k\).
\begin{choices} %%%%%%% begin choices
    \choice  9.027E+03\,V\(\cdot\) m
    \CorrectChoice 9.930E+03\,V\(\cdot\) m
    \choice  1.092E+04\,V\(\cdot\) m
    \choice  1.202E+04\,V\(\cdot\) m
    \choice  1.322E+04\,V\(\cdot\) m
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 5

\begin{questions} %%%%%%% begin questions

\question 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 3.5\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 6.171E+00\,N/C
    \choice  6.789E+00\,N/C
    \choice  7.467E+00\,N/C
    \choice  8.214E+00\,N/C
    \choice  9.036E+00\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  9.642E+00\,N/C
    \choice  1.061E+01\,N/C
    \CorrectChoice 1.167E+01\,N/C
    \choice  1.283E+01\,N/C
    \choice  1.412E+01\,N/C
\end{choices} %%% end choices

\question Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 7.6\,nano-Coulombs. What is the magnitude of the electric field at a distance of 5.8\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 1.017E+01\,N/C
    \choice  1.118E+01\,N/C
    \choice  1.230E+01\,N/C
    \choice  1.353E+01\,N/C
    \choice  1.488E+01\,N/C
\end{choices} %%% end choices

\question 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 2.8\,m from the center of the shells?
\begin{choices} %%%%%%% begin choices
    \choice  5.865E+00\,N/C
    \choice  6.451E+00\,N/C
    \choice  7.096E+00\,N/C
    \CorrectChoice 7.806E+00\,N/C
    \choice  8.587E+00\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.491E+01\,N/C
    \choice  1.640E+01\,N/C
    \CorrectChoice 1.804E+01\,N/C
    \choice  1.984E+01\,N/C
    \choice  2.182E+01\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  2.601E+01\,N/C
    \choice  2.861E+01\,N/C
    \choice  3.147E+01\,N/C
    \CorrectChoice 3.462E+01\,N/C
    \choice  3.808E+01\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  2.988E+00\,N/C
    \choice  3.287E+00\,N/C
    \choice  3.616E+00\,N/C
    \choice  3.977E+00\,N/C
    \CorrectChoice 4.375E+00\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  2.837E+01\,N/C
    \choice  3.121E+01\,N/C
    \choice  3.433E+01\,N/C
    \choice  3.776E+01\,N/C
    \CorrectChoice 4.154E+01\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  6.641E+00\,N/C
    \choice  7.305E+00\,N/C
    \CorrectChoice 8.036E+00\,N/C
    \choice  8.839E+00\,N/C
    \choice  9.723E+00\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  8.580E+00\,N/C
    \choice  9.438E+00\,N/C
    \choice  1.038E+01\,N/C
    \CorrectChoice 1.142E+01\,N/C
    \choice  1.256E+01\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 5.058E+00\,N/C
    \choice  5.564E+00\,N/C
    \choice  6.120E+00\,N/C
    \choice  6.732E+00\,N/C
    \choice  7.405E+00\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.096E+00\,N/C
    \choice  1.206E+00\,N/C
    \choice  1.327E+00\,N/C
    \choice  1.459E+00\,N/C
    \CorrectChoice 1.605E+00\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  2.964E+00\,N/C
    \choice  3.260E+00\,N/C
    \choice  3.586E+00\,N/C
    \CorrectChoice 3.944E+00\,N/C
    \choice  4.339E+00\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  3.251E+01\,N/C
    \choice  3.577E+01\,N/C
    \choice  3.934E+01\,N/C
    \choice  4.328E+01\,N/C
    \CorrectChoice 4.760E+01\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.114E+01\,N/C
    \CorrectChoice 1.225E+01\,N/C
    \choice  1.347E+01\,N/C
    \choice  1.482E+01\,N/C
    \choice  1.630E+01\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 9.592E+00\,N/C
    \choice  1.055E+01\,N/C
    \choice  1.161E+01\,N/C
    \choice  1.277E+01\,N/C
    \choice  1.404E+01\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  5.297E+00\,N/C
    \choice  5.827E+00\,N/C
    \choice  6.409E+00\,N/C
    \choice  7.050E+00\,N/C
    \CorrectChoice 7.755E+00\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  9.144E+00\,N/C
    \choice  1.006E+01\,N/C
    \choice  1.106E+01\,N/C
    \choice  1.217E+01\,N/C
    \CorrectChoice 1.339E+01\,N/C
\end{choices} %%% end choices

\question 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?
\begin{choices} %%%%%%% begin choices
    \choice  1.994E+01\,N/C
    \choice  2.194E+01\,N/C
    \choice  2.413E+01\,N/C
    \choice  2.655E+01\,N/C
    \CorrectChoice 2.920E+01\,N/C
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 6

\begin{questions} %%%%%%% begin questions

\question 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 \textrho(r)=ar\textsuperscript{1.6} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.4}. What is the magnitude of the electric field at a distance of 1.4\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  1.327E+02\,N/C
    \choice  1.460E+02\,N/C
    \choice  1.606E+02\,N/C
    \CorrectChoice 1.767E+02\,N/C
    \choice  1.943E+02\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=2.2\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.4} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.6}. What is the magnitude of the electric field at a distance of 0.86\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  4.874E+01\,N/C
    \CorrectChoice 5.362E+01\,N/C
    \choice  5.898E+01\,N/C
    \choice  6.488E+01\,N/C
    \choice  7.137E+01\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 2.2\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.604E+02\,N/C
    \choice  3.964E+02\,N/C
    \choice  4.360E+02\,N/C
    \choice  4.796E+02\,N/C
    \choice  5.276E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.2} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.8}. What is the magnitude of the electric field at a distance of 2.3\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  2.777E+02\,N/C
    \choice  3.055E+02\,N/C
    \CorrectChoice 3.361E+02\,N/C
    \choice  3.697E+02\,N/C
    \choice  4.066E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 1.5\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 1.383E+02\,N/C
    \choice  1.522E+02\,N/C
    \choice  1.674E+02\,N/C
    \choice  1.841E+02\,N/C
    \choice  2.025E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 3.0\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 7.825E+02\,N/C
    \choice  8.607E+02\,N/C
    \choice  9.468E+02\,N/C
    \choice  1.041E+03\,N/C
    \choice  1.146E+03\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.4} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.6}. What is the magnitude of the electric field at a distance of 1.5\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  1.123E+02\,N/C
    \choice  1.235E+02\,N/C
    \CorrectChoice 1.358E+02\,N/C
    \choice  1.494E+02\,N/C
    \choice  1.644E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.2} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.8}. What is the magnitude of the electric field at a distance of 2.7\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 4.782E+02\,N/C
    \choice  5.260E+02\,N/C
    \choice  5.787E+02\,N/C
    \choice  6.365E+02\,N/C
    \choice  7.002E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.2} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.8}. What is the magnitude of the electric field at a distance of 0.71\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 3.797E+01\,N/C
    \choice  4.177E+01\,N/C
    \choice  4.595E+01\,N/C
    \choice  5.054E+01\,N/C
    \choice  5.560E+01\,N/C
\end{choices} %%% end choices

\question A non-conducting sphere of radius R=1.4\,m has a non-uniform charge density that varies with the distnce from its center as given by \textrho(r)=ar\textsuperscript{1.6} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.4}. What is the magnitude of the electric field at a distance of 1.3\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 1.457E+02\,N/C
    \choice  1.603E+02\,N/C
    \choice  1.763E+02\,N/C
    \choice  1.939E+02\,N/C
    \choice  2.133E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.4} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.6}. What is the magnitude of the electric field at a distance of 2.6\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  3.821E+02\,N/C
    \choice  4.203E+02\,N/C
    \choice  4.624E+02\,N/C
    \CorrectChoice 5.086E+02\,N/C
    \choice  5.594E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 0.73\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 2.285E+01\,N/C
    \choice  2.514E+01\,N/C
    \choice  2.765E+01\,N/C
    \choice  3.042E+01\,N/C
    \choice  3.346E+01\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.4} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.6}. What is the magnitude of the electric field at a distance of 3.1\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  6.411E+02\,N/C
    \choice  7.052E+02\,N/C
    \CorrectChoice 7.757E+02\,N/C
    \choice  8.533E+02\,N/C
    \choice  9.386E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.7} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.3}. What is the magnitude of the electric field at a distance of 3.1\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  1.390E+03\,N/C
    \CorrectChoice 1.530E+03\,N/C
    \choice  1.682E+03\,N/C
    \choice  1.851E+03\,N/C
    \choice  2.036E+03\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 0.64\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  2.039E+01\,N/C
    \choice  2.243E+01\,N/C
    \CorrectChoice 2.467E+01\,N/C
    \choice  2.714E+01\,N/C
    \choice  2.985E+01\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.6} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.4}. What is the magnitude of the electric field at a distance of 0.76\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 2.406E+01\,N/C
    \choice  2.646E+01\,N/C
    \choice  2.911E+01\,N/C
    \choice  3.202E+01\,N/C
    \choice  3.522E+01\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.8} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.2}. What is the magnitude of the electric field at a distance of 1.7\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \CorrectChoice 2.079E+02\,N/C
    \choice  2.287E+02\,N/C
    \choice  2.516E+02\,N/C
    \choice  2.767E+02\,N/C
    \choice  3.044E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.5} (r\(x\)R) where a=3\,nC\(\cdot\) m\textsuperscript{-1.5}. What is the magnitude of the electric field at a distance of 1.7\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  2.579E+02\,N/C
    \CorrectChoice 2.837E+02\,N/C
    \choice  3.121E+02\,N/C
    \choice  3.433E+02\,N/C
    \choice  3.776E+02\,N/C
\end{choices} %%% end choices

\question 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 \textrho(r)=ar\textsuperscript{1.2} (r\(x\)R) where a=2\,nC\(\cdot\) m\textsuperscript{-1.8}. What is the magnitude of the electric field at a distance of 2.1\,m from the center? 
\begin{choices} %%%%%%% begin choices
    \choice  2.274E+02\,N/C
    \choice  2.501E+02\,N/C
    \CorrectChoice 2.751E+02\,N/C
    \choice  3.026E+02\,N/C
    \choice  3.329E+02\,N/C
\end{choices} %%% end choices
\end{questions}
\pagebreak

\section{Attribution}
\theendnotes
\end{document}

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