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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {B}}=}$

 −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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where${\displaystyle {\mathcal {F}}=}$

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {A}}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {F}}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {C}}=}$:

 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)?
${\displaystyle Answer}$ (assuming ${\displaystyle {\mathcal {B}}>{\mathcal {A}}}$) ${\displaystyle is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}}$, where ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

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