# User:Guy vandegrift/Quizbank/Archive1/Calculus Physics/T1study

## CalcPhysIIT1_Study

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This document contains either a study guide OR pairs of exams taken from the same exam bank
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### CalcPhysIIT1_Study-v1s1

1. Integrate the line integral of, ${\displaystyle {\vec {F}}=8.3xy{\hat {x}}+8.6y^{3}{\hat {y}}}$, along the y axis from y = 4 to y = 16

___ a) 1.31E+05
___ b) 1.40E+05
___ c) 1.50E+05
___ d) 1.61E+05
___ e) 1.72E+05

2. Integrate the function, ${\displaystyle {\vec {F}}=r^{9}\theta ^{5}{\hat {r}}+r^{8}\theta ^{7}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 4

___ a) 1.14E+06
___ b) 1.21E+06
___ c) 1.30E+06
___ d) 1.39E+06
___ e) 1.49E+06

3. Integrate the line integral of ${\displaystyle {\vec {F}}=3.3xy{\hat {x}}+8.7x{\hat {y}}}$ from the origin to the point at x = 2.1 and y = 3.2

___ a) 4.18E+01
___ b) 4.48E+01
___ c) 4.79E+01
___ d) 5.12E+01
___ e) 5.48E+01

4. Integrate the function, ${\displaystyle {\vec {F}}=-x^{3}y^{4}{\hat {x}}+x^{4}y^{4}{\hat {y}}}$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule

___ a) 3.43E-01
___ b) 3.67E-01
___ c) 3.93E-01
___ d) 4.21E-01
___ e) 4.50E-01

5. What is the magnitude of the electric field at the origin if a 3.1 nC charge is placed at x = 6.2 m, and a 2.6 nC charge is placed at y = 6 m?

___a) 5.47 x 10-1N/C
___b) 6.32 x 10-1N/C
___c) 7.3 x 10-1N/C
___d) 8.43 x 10-1N/C
___e) 9.73 x 10-1N/C

6. What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8 m, and a 1.4 nC charge is placed at y = -9.3 m?

___a) 2.37 x 101degrees
___b) 2.74 x 101degrees
___c) 3.16 x 101degrees
___d) 3.65 x 101degrees
___e) 4.22 x 101degrees

7. A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a2, where β equals

___a) 7.31 x 10-3 unit
___b) 8.86 x 10-3 unit
___c) 1.07 x 10-2 unit
___d) 1.3 x 10-2 unit
___e) 1.57 x 10-2 unit

8. A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a2, where β equals

___a) 2.36 x 10-1 unit
___b) 2.86 x 10-1 unit
___c) 3.47 x 10-1 unit
___d) 4.2 x 10-1 unit
___e) 5.09 x 10-1 unit

9. 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 ${\displaystyle {\mathcal {B}}=}$

___ a) −7
___ b) 3
___ c) −3
___ d) −3
___ e) 2

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 ${\displaystyle {\mathcal {C}}=}$:

___ a) s−4
___ b) 5−s
___ c) 1−s
___ d) s−1
___ e) 5

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 ${\displaystyle {\mathcal {F}}=}$:

___ a) 3/2
___ b) 1/2
___ c) 3
___ d) 2
___ e) 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 ${\displaystyle {\mathcal {C}}=}$:

___ a) s−7
___ b) 8
___ c) 3−s
___ d) 7−s
___ e) s−3

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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

___ a) 32 + 82
___ b) (7-s)2 + 82
___ c) 72 + (8−s)2
___ d) 72 + (3−s)2
___ e) 72 + 82

14. 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 ${\displaystyle {\mathcal {C}}=}$

___ a) s−7
___ b) s−3
___ c) 3
___ d) 7−s
___ e) 3−s

15. 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${\displaystyle {\mathcal {F}}=}$

___ a) 2
___ b) 1/2
___ c) 3/2
___ d) 3

16. 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 ${\displaystyle {\mathcal {C}}=}$:

___ a) s − 9
___ b) 2
___ c) 9 − s
___ d) 2 − s
___ e) s − 2

17. 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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

___ a) 92 + (2-s)2
___ b) 92 + (7-s)2
___ c) 72 + (2-s)2
___ d) 22 + (9-s)2
___ e) 22 + (7-s)2

18. 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 ${\displaystyle {\mathcal {A}}=}$:

___ a) 1/2
___ b) 2
___ c) 8
___ d) 4

19. 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 ${\displaystyle {\mathcal {C}}=}$:

___ a) 4
___ b) s−4
___ c) 8−s
___ d) 4−s
___ e) s−8

20. 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 ${\displaystyle {\mathcal {C}}=}$:

___ a) s−4
___ b) 8−s
___ c) s−8
___ d) 4
___ e) 4−s

21. 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 ${\displaystyle {\mathcal {C}}=}$:

___ a) s−4
___ b) s−1
___ c) 1−s
___ d) 5−s
___ e) 5

22. A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

___ a)c) ${\displaystyle \varepsilon _{0}E=H\rho z}$
___ b)d) none of these are correct
___ c)e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
___ d) ${\displaystyle \varepsilon _{0}E=\rho z}$
___ e)b) ${\displaystyle \varepsilon _{0}E=H\rho }$

23. A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

___ a)b) none of these are correct
___ b)e) ${\displaystyle \varepsilon _{0}E=H\rho z}$
___ c)d) ${\displaystyle \varepsilon _{0}E=H\rho }$
___ d)c) ${\displaystyle \varepsilon _{0}E=\rho z}$
___ e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

24. A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

___ a) none of these are correct
___ b)d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
___ c)e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
___ d)c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
___ e)b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

25. A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

___ a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
___ b)b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
___ c)d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
___ d)c) none of these are correct
___ e)e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

26. A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

___ a)b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
___ b)d) none of these are correct
___ c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
___ d)c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
___ e)e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

27. A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

___ a) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
___ b)b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
___ c)c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
___ d)e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
___ e)d) none of these are correct

#### Key to CalcPhysIIT1_Study-v1s1

1. Integrate the line integral of, ${\displaystyle {\vec {F}}=8.3xy{\hat {x}}+8.6y^{3}{\hat {y}}}$, along the y axis from y = 4 to y = 16

- a) 1.31E+05
+ b) 1.40E+05
- c) 1.50E+05
- d) 1.61E+05
- e) 1.72E+05

2. Integrate the function, ${\displaystyle {\vec {F}}=r^{9}\theta ^{5}{\hat {r}}+r^{8}\theta ^{7}{\hat {\theta }}}$ , along the first quadrant of a circle of radius 4

- a) 1.14E+06
+ b) 1.21E+06
- c) 1.30E+06
- d) 1.39E+06
- e) 1.49E+06

3. Integrate the line integral of ${\displaystyle {\vec {F}}=3.3xy{\hat {x}}+8.7x{\hat {y}}}$ from the origin to the point at x = 2.1 and y = 3.2

- a) 4.18E+01
+ b) 4.48E+01
- c) 4.79E+01
- d) 5.12E+01
- e) 5.48E+01

4. Integrate the function, ${\displaystyle {\vec {F}}=-x^{3}y^{4}{\hat {x}}+x^{4}y^{4}{\hat {y}}}$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule

- a) 3.43E-01
- b) 3.67E-01
- c) 3.93E-01
- d) 4.21E-01
+ e) 4.50E-01

5. What is the magnitude of the electric field at the origin if a 3.1 nC charge is placed at x = 6.2 m, and a 2.6 nC charge is placed at y = 6 m?

-a) 5.47 x 10-1N/C
-b) 6.32 x 10-1N/C
-c) 7.3 x 10-1N/C
-d) 8.43 x 10-1N/C
+e) 9.73 x 10-1N/C

6. What angle does the electric field at the origin make with the x-axis if a 2 nC charge is placed at x = -8 m, and a 1.4 nC charge is placed at y = -9.3 m?

-a) 2.37 x 101degrees
+b) 2.74 x 101degrees
-c) 3.16 x 101degrees
-d) 3.65 x 101degrees
-e) 4.22 x 101degrees

7. A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 4a, 2a) is βkQ/a2, where β equals

-a) 7.31 x 10-3 unit
-b) 8.86 x 10-3 unit
-c) 1.07 x 10-2 unit
-d) 1.3 x 10-2 unit
+e) 1.57 x 10-2 unit

8. A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a2, where β equals

-a) 2.36 x 10-1 unit
-b) 2.86 x 10-1 unit
+c) 3.47 x 10-1 unit
-d) 4.2 x 10-1 unit
-e) 5.09 x 10-1 unit

9. 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 ${\displaystyle {\mathcal {B}}=}$

- a) −7
- b) 3
- c) −3
- d) −3
+ e) 2

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 ${\displaystyle {\mathcal {C}}=}$:

- a) s−4
- b) 5−s
+ c) 1−s
- d) s−1
- e) 5

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 ${\displaystyle {\mathcal {F}}=}$:

+ a) 3/2
- b) 1/2
- c) 3
- d) 2
- e) 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 ${\displaystyle {\mathcal {C}}=}$:

- a) s−7
- b) 8
- c) 3−s
+ d) 7−s
- e) s−3

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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

- a) 32 + 82
+ b) (7-s)2 + 82
- c) 72 + (8−s)2
- d) 72 + (3−s)2
- e) 72 + 82

14. 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 ${\displaystyle {\mathcal {C}}=}$

- a) s−7
- b) s−3
- c) 3
+ d) 7−s
- e) 3−s

15. 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${\displaystyle {\mathcal {F}}=}$

- a) 2
- b) 1/2
+ c) 3/2
- d) 3

16. 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 ${\displaystyle {\mathcal {C}}=}$:

- a) s − 9
- b) 2
+ c) 9 − s
- d) 2 − s
- e) s − 2

17. 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 ${\displaystyle {\mathcal {D}}^{2}+{\mathcal {E}}^{2}=}$:

- a) 92 + (2-s)2
- b) 92 + (7-s)2
- c) 72 + (2-s)2
+ d) 22 + (9-s)2
- e) 22 + (7-s)2

18. 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 ${\displaystyle {\mathcal {A}}=}$:

- a) 1/2
- b) 2
- c) 8
+ d) 4

19. 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 ${\displaystyle {\mathcal {C}}=}$:

+ a) 4
- b) s−4
- c) 8−s
- d) 4−s
- e) s−8

20. 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 ${\displaystyle {\mathcal {C}}=}$:

- a) s−4
+ b) 8−s
- c) s−8
- d) 4
- e) 4−s

21. 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 ${\displaystyle {\mathcal {C}}=}$:

- a) s−4
- b) s−1
- c) 1−s
- d) 5−s
+ e) 5

22. A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z > H/2?

- a)c) ${\displaystyle \varepsilon _{0}E=H\rho z}$
- b)d) none of these are correct
+ c)e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$
- d) ${\displaystyle \varepsilon _{0}E=\rho z}$
- e)b) ${\displaystyle \varepsilon _{0}E=H\rho }$

23. A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much less than the radius: H << R. The electric field at the center vanishes. What formula describes the electric field at a distance, z, on axis from the center if z < H/2?

- a)b) none of these are correct
- b)e) ${\displaystyle \varepsilon _{0}E=H\rho z}$
- c)d) ${\displaystyle \varepsilon _{0}E=H\rho }$
+ d)c) ${\displaystyle \varepsilon _{0}E=\rho z}$
- e) ${\displaystyle \varepsilon _{0}E=H\rho /2}$

24. A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius or R. What formula describes the electric field at a distance r > R?

- a) none of these are correct
- b)d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
+ c)e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
- d)c) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
- e)b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

25. A sphere has a uniform charge density of ${\displaystyle \rho }$, and a radius equal to R. What formula describes the electric field at a distance r < R?

- a) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /2}$
- b)b) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /3}$
+ c)d) ${\displaystyle r^{2}\varepsilon _{0}E=r^{3}\rho /3}$
- d)c) none of these are correct
- e)e) ${\displaystyle r^{2}\varepsilon _{0}E=R^{3}\rho /2}$

26. A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r < R?

- a)b) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
- b)d) none of these are correct
- c) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
+ d)c) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
- e)e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$

27. A cylinder of radius, R, and height H has a uniform charge density of ${\displaystyle \rho }$. The height is much greater than the radius: H >> R. The electric field at the center vanishes. What formula describes the electric field at a distance, r, radially from the center if r > R?

- a) ${\displaystyle 2R\varepsilon _{0}E=r^{2}\rho }$
- b)b) ${\displaystyle 2\varepsilon _{0}E=r\rho }$
+ c)c) ${\displaystyle 2r\varepsilon _{0}E=R^{2}\rho }$
- d)e) ${\displaystyle 2r^{2}\varepsilon _{0}E=R^{3}\rho }$
- e)d) none of these are correct