Physics equations/18-Electric charge and field/Q:lineChargesCALCULUS/Quizbank

1 A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {B}}=$

	−7
	−3
	−3
	3
	2

2 A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$

	3−s
	3
	s−7
	7−s
	s−3

3 A line of charge density λ situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where${\mathcal {F}}=$

	2
	3
	3/2
	1/2

4 A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

	2
	s − 2
	2 − s
	s − 9
	9 − s

5 A line of charge density λ situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

	92 + (7-s)2
	92 + (2-s)2
	72 + (2-s)2
	22 + (7-s)2
	22 + (9-s)2

6 A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {A}}=$:

	1/2
	4
	2
	8

7 A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

	s−8
	8−s
	s−4
	4−s
	4

8 A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

	s−8
	8−s
	s−4
	4−s
	4

9 A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

	5
	s−4
	5−s
	1−s
	s−1

10 A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

	5
	s−4
	5−s
	1−s
	s−1

11 A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

	1/2
	2/3
	2
	3/2
	3

12 A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

	s−3
	3−s
	8
	s−7
	7−s

13 A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {D}}^{2}+{\mathcal {E}}^{2}=$:

	72 + (8−s)2
	72 + 82
	(7-s)2 + 82
	72 + (3−s)2
	32 + 82