Physics 72: Chapter 22 Problem Set Summer 2010

Name: Score:

Lecturer: Mr Carlos Baldo III Section: X7-7

Encircle the letter of the correct answer. Solve each problem clearly and completely for full credit.

For the next two numbers, consider the figures below. Three charged objects (L, M, & N) of equal charges (7nC) but

different radii are each surrounded concentrically by the identical Gaussian (dashed) surfaces (all have radius R) as

shown below.

1. Rank the objects in terms of their electric flux.

A. L>M>N

B. L<M<N

C. L=M=N=0

D. L=M=N≠0

E. Cannot be determined

2. Rank the objects in terms of their electric field on the Gaussian surfaces.

A. L>M>N

B. L<M<N

C. L=M=N=0

D. L=M=N≠0

E. Cannot be determined

3. A negative point charge is placed at the center of a Gaussian spherical surface. Which of the following will probably

happen if another negative point charge is placed near but outside the Gaussian surface?

A. Only the electric flux through the Gaussian surface will change

B. Only the electric field on the Gaussian surface will change

C. Both the electric flux and the electric field will change

D. Both the electric flux and the electric field will not change

E. Can not be determined

4. The figure below shows three Gaussian surfaces that encloses some charges. Which of the following correctly

ranks their net electric flux?

A. X>Y>Z

B. X<Y<Z

C. Y>X>Z

D. Y<X<Z

E. Cannot be determined

For the next two numbers, consider two charges (+Q & -Q) and a point, P, show below

5. What is (are) the simplest Gaussian surface(s) that can be

used to manually calculate the electric field at Point P?

A. One cylinder centered at Point P

B. One Sphere centered at Point P

C. One Sphere centered at the (-)

D. Two spheres - one centered at the (+), another at the (-)

E. Two cylinders - one centered at the (+), another at the (-)

6. What is the net electric field at Point P?

A. Q/(16ϵ0пa2) – Q/(4ϵ0пa2), to the right

B. Q/(16ϵ0пa2) – Q/(4ϵ0пa2), to the left

C. Q/(16ϵ0пa2) + Q/(4ϵ0пa2), to the right

D. Q/(16ϵ0пa2) + Q/(4ϵ0пa2), to the left

E. Q/(16ϵ0пa2) – Q/(16ϵ0пa2), to the right

Physics 72: Chapter 22 Problem Set Summer 2010

7. Consider two infinite line of linear charge density +λ & +2λ and a point, P, located exactly between them as show

below. What is the net electric field at Point P?

A. λ /(2пϵ0L) directed upward

B. λ /(2пϵ0L) directed downward

C. 3λ /(2ϵ0L) directed upward

D. 3λ /(ϵ0L) directed downward

E. The problem is asymmetric thus; Gauss law cannot be used to

manually solve the given problem

8. Consider a solid spherical conductor of radius R and charge +Q at electrostatic equilibrium

shown at the right. Which is the correct ranking of the Points A, B, C, and D according the

value of the electric field at their locations?

A. D > C > B > A

B. D > C > B = A

C. D = C > B > A

D. D = C > B = A

E. D < C < B < A

9. Consider an initially uncharged metal sphere with a negative charge (-Q) inside the cavity at its center. What is the

electric field at point Y which is at a distance y from the center?

A. 0

B. Any constant value.

C. Q/(4ϵ0пy2) away from the center

D. Q/(4ϵ0пy2) toward the center

E. It depends on the charge at the inner and outer surface of the sphere

10. Consider a charge +2nC placed inside the cavity of an initially uncharged conducting cubic shell. At electrostatic

equilibrium, which of the following is true about the charges in the cube’s surfaces?

A. Inside:0nC; Outside: 0nC

B. Inside:-2nC; Outside: 0nC

C. Inside:-2nC; Outside: +2nC

D. Inside:+2nC; Outside: -2nC

E. Inside:-1nC; Outside: -1nC

For the next two numbers, consider a hollow thin spherical shell of radius R and total charge +q. A point charge –q is

located a distance 2R away from the center of the shell.

11. If the shell is insulating and the charge +q is uniformly distributed, what is the magnitude of the net electric field

at the center of the shell?

A. Zero

B. 2

4

kq

R

C. 2

kq

R

D. 2

2kq

R

E. 2

5

4

kq

R

12. If the shell is conducting and equilibrium has been established, what is the magnitude of the electric field at its

center?

A. Zero

B. 2

4

kq

R

C. 2

kq

R

D. 2

2kq

R

E. 2

5

4

kq

R

Physics 72: Chapter 22 Problem Set Summer 2010

For the next four numbers, consider two hollow concentric conducting spheres. The innermost sphere has a net charge

+10nC while the outermost sphere is uncharged.

13. At electrostatic equilibrium, what are the net charges on the inner and outer surfaces of the outer hollow sphere?

A. Zero, zero

B. +5 nC, -5 nC

C. -5 nC, +5 nC

D. +10 nC, - 10 nC

E. –10 nC, +10 nC

14. What is the net electric field in the cavity between the two spheres at a distance r from the center of the spheres?

A. Zero

B. 5 nC / (4πεor2); towards the small hollow sphere

C. 5 nC / (4πεor2); away the small hollow sphere

D. 10 nC / (4πεor2); towards the small hollow sphere

E. 10 nC / (4πεor2); away the small hollow sphere

15. If a +5 nC point charge is placed at the center of the two hollow spheres, what are the net charges on the inner and

outer surfaces of the outer hollow sphere at equilibrium?

A. Zero, zero

B. +10 nC, -10 nC

C. -10 nC, +10 nC

D. +15 nC, - 15 nC

E. –15 nC, +15 nC

16. What is the net electric field in the cavity between the two hollow spheres at a distance r from the center of the

spheres?

A. Zero

B. 10 nC / (4πεor2); towards the small hollow sphere

C. 10 nC / (4πεor2); away the small hollow sphere

D. 15 nC / (4πεor2); towards the small hollow sphere

E. 15 nC / (4πεor2); away the small hollow sphere

For the next three numbers, consider a charge –5q placed inside the cavity of an initially uncharged conducting

spherical shell

17. After the system has electrostatic equilibrium, what is the induced net charge in the outer surface of the

spherical shell?

A. Zero

B. – 5 q

C. +5q

D. – 10q

E. + 10q

18. If the outside of the shell is then grounded, by connecting a conducting wire between the shell and the earth, what

are the induced charges on the inside and outside surfaces of the shell?

A. -5q inside, zero outside

B. zero inside, -5q outside

C. +5q inside, zero outside

D. zero inside, +5q outside

E. Both zero inside and outside

19. After the grounding process, what would be the magnitude of the electric field outside the shell?

Physics 72: Chapter 22 Problem Set Summer 2010

A. Zero

B. 2R

kq

C. 2

5

R

kq

D. 2

10

R

kq

E. 2

15

R

kq

20. Which of the following statements is FALSE?

A. In electrostatic equilibrium condition, the electric field inside a charged conductor is zero.

B. Excess charges accumulate at the surfaces of a charged conductor.

C. The magnitude of the electric field on the surface of a cubic charged conductor is constant.

D. The electric field vector on the surface of a charged conductor has no tangential component to the surface

of the conductor.

E. The net electric flux through a Gaussian surface that is enclosing a charged conductor changes once a point

charge is placed inside it.

21. A uniformly charged solid sphere of radius 1.00 cm generates an electric field of magnitude 1.0 N/C at a distance of

2.00 cm away from its center. What is the magnitude of the field 4.00 cm from the center?

A. 1.0 N/C

B. 0.50 N/C

C. 0.30 N/C

D. 0.25 N/C

E. 0.10 N/C

22. Consider a conducting shell with total charge +2Q. If a positive +Q charge is placed at the center of the shell, what

are the charges on the outer and inner surfaces of the shell?

A. –Q, +Q

B. –Q, +2Q

C. –Q, +3Q

D. Zero, +2Q

E. Zero, +3Q

23. Which of the following statements is always TRUE?

A. Zero net electric flux implies that there is no charge inside a Gaussian surface.

B. Gauss’ law holds only for symmetric charge distributions.

C. The result that E = 0 in a conductor under electrostatic condition can be derived from Gauss’ law.

D. If the net electric flux is zero, then the electric field at every point on a Gaussian surface is zero.

E. The net electric flux decreases as the size of the Gaussian surface increases

24. A point charge q1 = +4.00 nC is located on the x-axis at x = +2.00 m. A second point charge q2 = -6.00 nC is on the y-

axis at y = +1.00 m. What is the total electric flux due to these two point charges through a spherical surface

centered at the origin and with radius 2.50 m?

A. +10.00 nC/εo

B. +4.00 nC/εo

C. Zero

D. -2.00 nC/εo

E. -6.00 nC/εo

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