Voltage and Capacitance

Voltage and Capacitance Practice Test

Helpful Hints: Voltage: Use V=-E∙dr when you want to find voltage between charged objects. Use V=dq4πϵ0r when you want to find the voltage at a point due to a charge distribution. Gauss’s Law with dielectrics: E∙dA= qencκϵ0

For capacitors: C= Q/V and U= 12CV2

1-6: Multiple choice

1-2  A hollow conducting sphere has charge +Q on it.

1.  Which of the following graphs best describes E vs r?

A) D)

B) E)

C)

2.  Which of the preceding graphs best describes V vs r?

3.  Two very large, oppositely charged conducting plates are separated by a small distance d. Which of the following will increase if d is increased?

I.  Electric field between the plates

II.  The voltage across the plates

III.  The capacitance

A)  I only D) II and III

B)  II only E) I, II and III

C)  III only

4-6: The diagram at the right shows

a cross-section of equipotential

surfaces.

4.  Which point has the largest

magnitude E field?

A)  A

B)  B

C)  C

D)  D

E)  E

5.  The work required to move a positive charge from point D to point C is

A)  0 D) Impossible to determine

B)  0

C)  = 0

6.  The magnitude of the work required to move 0.50 coulomb of charge from point B to point A is

A)  30 J D) 15 V

B)  15 J E) Impossible to determine

C)  7.5 J

7.  Consider a hollow, insulating

hemisphere of radius R with uniformly

distributed charge +Q.

A)  Find the voltage at point P, located

at the center of curvature of the hemisphere.

B) How fast would a proton that was released from rest at point P be traveling by the time it gets very far away from the hemisphere? Let R = 0.15 m, Q = 2.0 x 10-12 C, mproton = 1.67 x 10-27 kg, and qproton = 1.6 x 10-19 C.

8.  A spherical capacitor with dielectric

is shown at right in cross-section. The

inner conducting sphere has charge +Q,

while the outer conducting sphere has

charge –Q.

A) Use Gauss’ Law to find E

for a r b (include k)

B)  Find Va - Vb

C)  Find the capacitance.

9.  Two capacitors C1 and C2 are charged in parallel up to a voltage Vo. (Remember that “in parallel” means that they have the same voltage across them.) C2 is then disconnected and flipped, so that its + terminal is connected to C1’s – terminal as shown.

When the switch is closed:

A)  Find the final voltage Vf across C1 and C2. Hint: Draw the circuit after the switch has closed…

B)  Find the ratio of final to initial electrical potential energy.

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