Question 1

A positive charge $$Q is $$uniformly distributed along the x-axis from $$x = a to$$ $$x = b. $$What is the expression for the electric potential at the origin due to this distribution? (Assume $$k is $$Coulomb's constant.)

Accepted Answer

$$V = kQ \int_a^b \frac{dx}{x}$$

Question 2

Two capacitors, $$C_1 = 2.0$$\ \mu\mathrm{F}$$ and C_2$ = 4.0\ \mu\mathrm{F}$$, are connected in series to a $$6.0\ \mathrm{V}$$ battery. What is the charge on each capacitor?

Accepted Answer

$$Q = 4\ \mu\mathrm{C}$$

Question 3

If the separation between the plates of a charged capacitor connected to a battery is halved, how does the capacitance change?

Accepted Answer

It doubles

Question 4

A $$2.0\ \mu\mathrm{F}$$ and a $$4.0\ \mu\mathrm{F}$$ capacitor are connected in series to a $$6.0\ \mathrm{V}$$ battery. What is the potential difference across the $$2.0\ \mu\mathrm{F}$$ capacitor?

Accepted Answer

$$4.0\ \mathrm{V}$$

Question 5

If the separation between the plates of a charged capacitor connected to a battery is halved, how does the charge on the capacitor change?

Accepted Answer

It doubles

Question 6

Wire A and wire B are connected in series. If the diameter of wire A is three times that of wire B, how does the electron drift speed $$v_{dA} in $$wire A compare with $$v_{dB} in $$wire B?

Accepted Answer

$$v_{dA} = \frac{1}{9} v_{dB}$$

Question 7

The potential at the surface of a solid metal sphere of radius $$a is$$ $$V_0. $$What is the potential at a point of distance $$b \u003e a$$ from the center of the sphere?

Accepted Answer

$$V = V_0$ \frac{a}{b}$$

Question 8

A small insulating solid sphere with radius $$a is $$concentric with a larger conducting spherical shell with inner radius $$b$$ and outer radius $$c. $$The solid sphere has total charge $$-q$$ distributed uniformly over the entire volume, and the shell has charge $$-4q. $$What is the electric field for $$r \u003c a$$?

Accepted Answer

$$E = \frac{1}{4\pi\$$epsilon_0$$} \frac{-q r}{a^3$}$$

Question 9

If the separation between the plates of a charged capacitor connected to a battery is halved, by what factor does the energy stored change?

Accepted Answer

It doubles

Question 10

Paper with dielectric constant $$k = 4.0 is $$inserted between the plates of a capacitor, filling the gap. How does the capacitance change?

Accepted Answer

It increases by a factor of 4

Question 11

A parallel-plate capacitor is connected to a battery and then disconnected. If the plate separation is halved, what happens to the voltage across the plates?

Accepted Answer

It halves

Question 12

A parallel-plate capacitor is connected to a battery. If the plate separation is halved while still connected, what happens to the electric field between the plates?

Accepted Answer

It remains the same

Question 13

A parallel-plate capacitor is connected to a battery. If the plate separation is halved while still connected, what happens to the charge on the capacitor?

Accepted Answer

It doubles

Question 14

A parallel-plate capacitor is connected to a battery. If the plate separation is halved while still connected, what happens to the potential difference across the plates?

Accepted Answer

It remains the same

Question 15

A parallel-plate capacitor is connected to a battery. If the plate separation is halved while still connected, what happens to the energy stored in the capacitor?

Accepted Answer

It doubles

Question 16

A parallel-plate capacitor is disconnected from a battery and the plate separation is halved. What happens to the charge on the capacitor?

Accepted Answer

It remains the same

Physics with Calculus Exam 2 Review – Electrostatics, Capacitance, and Gauss’s Law

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