Question 1

A parallel-plate capacitor has a uniform electric field between its plates. If the electric field strength is $$E$$ and the distance from the negative plate is $$s$$, what is the electric potential at point $$s ($$assuming $$V = 0 at $$the negative plate)?

Accepted Answer

$$V = Es$$

Question 2

Given the potential of a point charge is $$V = \frac{q}{4\pi \$$epsilon_0$$ r}$$, what is the electric field at a distance $$r$$ from the charge?

Accepted Answer

$$E = -\frac{dV}{dr} = \frac{q}{4\pi \$$epsilon_0$$ r^2$}$$

Question 3

The on-axis potential of a ring of radius $$R$$ and charge $$Q is$$ $$V_{ring} = \frac{1}{4\pi \$$epsilon_0$$} \frac{Q}{\sqrt{z^2$ + R^2$}}. $$What is the on-axis electric field at position $$z$$?

Accepted Answer

$$E_z = -\frac{dV_{ring}}{dz} = \frac{1}{4\pi \$$epsilon_0$$} \frac{Qz}{(z^2$ + R^2$)^{3/2}$$}$

Question 4

If the electric potential $$V$$ varies with position $$x as $$shown in a graph, what is the relationship between the electric field $$E_x$$ and the slope of the potential graph?

Accepted Answer

$$E_x = -\frac{dV}{dx}$$

Question 5

A region of space has a constant electric potential. What is the electric field in this region?

Accepted Answer

$$E = 0$$

Question 6

Which statement about the electric field inside a conductor in electrostatic equilibrium is correct?

Accepted Answer

The electric field inside is zero.

Question 7

Two metal spheres are connected by a metal wire. Which quantities do they have in common?

Accepted Answer

Same potential

Question 8

A battery does $$4.8 	imes 10$$^{-19}$$ J of work for each positive ion moved from the negative to the positive terminal. What is the battery's emf?

Accepted Answer

$$4.8 V$$

Question 9

If two $$1.5 V $$batteries are connected in series, what is the total potential difference across both batteries?

Accepted Answer

$$3.0 V$$

Question 10

The capacitance $$C of a $$parallel-plate capacitor depends on which of the following?

Accepted Answer

The surface area of the plates and the spacing between them

Question 11

What is the charge $$Q on a $$capacitor with capacitance $$C$$ and potential difference $$V$$?

Accepted Answer

$$Q = CV$$

Question 12

Three capacitors with capacitances $$C_1$$, $$C_2$$, and $$C_3$$ are connected in parallel. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = C_1$ + C_2$ + C_3$

Question 13

Three capacitors with capacitances $$C_1$$, $$C_2$$, and $$C_3$$ are connected in series. What is the equivalent capacitance?

Accepted Answer

$$\frac{1}{C_{eq}} = \frac{1}{C_1$} + \frac{1}{C_2$} + \frac{1}{C_3$}$$

Question 14

What is the energy $$U$$ stored in a capacitor with capacitance $$C$$ and voltage $$V$$?

Accepted Answer

$$U = \frac{1}{2}CV^2$

Question 15

A capacitor charged to $$1.5 V $$stores $$2.0 mJ of $$energy. If the capacitor is charged to $$3.0 V$$, how much energy will it store?

Accepted Answer

$$8.0 mJ$$

Question 16

What is the energy density $$u of $$the electric field inside a parallel-plate capacitor?

Accepted Answer

$$u = \frac{1}{2}\$$epsilon_0$$ E^2$

Question 17

A charged particle of mass $$m$$ and charge $$q is $$placed in a uniform electric field $$E. $$What is its acceleration?

Accepted Answer

$$a = \frac{qE}{m}$$

Question 18

A dipole placed in a uniform electric field experiences which of the following?

Accepted Answer

A torque that tends to align the dipole with the field

Question 19

According to Kirchhoff's loop law, what is the sum of all potential differences encountered while moving around a closed loop?

Accepted Answer

Zero

Electric Potential, Electric Field, and Capacitance: Study Notes

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