Free AP® Physics C: Electricity and Magnetism Practice Test

Question 1

A solid insulating sphere of radius R carries charge Q spread uniformly through its volume. The field at its surface has magnitude E₀. What is the field magnitude at a distance R/2 from the center?

Accepted Answer

E₀/2

Answer

E₀/4

Answer

E₀

Answer

4E₀

Question 2

A capacitor charged to 10 V is disconnected from its battery and allowed to discharge through a resistor. What is the capacitor’s voltage after one time constant?

Accepted Answer

3.7 V

Answer

0 V

Answer

5.0 V

Answer

6.3 V

Question 3

What is the electric potential 0.30 m from a 2.0 nC point charge, taking V = 0 at infinity? (k = 9.0 × 10⁹ N·m²/C²)

Accepted Answer

60 V

Answer

6.0 V

Answer

18 V

Answer

20 V

Question 4

A charged particle moves in a circle at right angles to a uniform magnetic field. If its speed is doubled, what happens to the radius of its circle and the time for one revolution?

Accepted Answer

The radius doubles, and the period stays the same.

Answer

Both double.

Answer

The radius stays the same, and the period is halved.

Answer

The radius is halved, and the period stays the same.

Question 5

A metal bar 0.50 m long slides at 4.0 m/s along two parallel rails joined by a 2.0 Ω resistor, in a uniform 0.20 T field perpendicular to the rails. Ignoring the resistance of the rails and bar, what current flows?

Accepted Answer

0.20 A

Answer

1.6 A

Answer

0.80 A

Answer

0.050 A

Question 6

A 3.0 μF capacitor and a 6.0 μF capacitor are connected in series across a 12 V battery. How much charge is on the 3.0 μF capacitor once it is fully charged?

Accepted Answer

24 μC

Answer

108 μC

Answer

72 μC

Answer

36 μC

Question 7

Charge +4.0 μC sits at x = 0 and charge +1.0 μC sits at x = 3.0 m. At what point on the x-axis is the electric field zero?

Accepted Answer

x = 2.0 m

Answer

x = 6.0 m

Answer

x = 1.5 m

Answer

x = 1.0 m

Question 8

A battery with an emf of 12 V and an internal resistance of 1.0 Ω is connected to a 5.0 Ω resistor. What is the potential difference across the battery’s terminals?

Accepted Answer

10 V

Answer

2.0 V

Answer

12 V

Answer

14 V

Question 9

In a region, the electric potential along the x-axis is V(x) = 3x² − 2x, with V in volts and x in meters. What is the x-component of the electric field at x = 1.0 m?

Accepted Answer

−4.0 V/m

Answer

4.0 V/m

Answer

1.0 V/m

Answer

−6.0 V/m

Question 10

A circular loop of wire with a radius of 0.10 m carries a current of 5.0 A. What is the magnetic field at its center? (μ₀ = 4π × 10⁻⁷ T·m/A)

Accepted Answer

3.1 × 10⁻⁵ T

Answer

1.0 × 10⁻⁵ T

Answer

6.3 × 10⁻⁵ T

Answer

3.1 × 10⁻⁷ T

Question 11

A closed cube encloses a +2.0 nC point charge, and a +5.0 nC point charge sits just outside the cube. What is the net electric flux through the cube’s surface? (ε₀ = 8.85 × 10⁻¹² C²/N·m²)

Accepted Answer

2.3 × 10² N·m²/C

Answer

0 N·m²/C

Answer

5.6 × 10² N·m²/C

Answer

7.9 × 10² N·m²/C

Question 12

A 12 V battery, a 4.0 Ω resistor and a 2.0 H inductor are connected in series, and the switch is closed at t = 0. At what rate is the current increasing just after the switch closes?

Accepted Answer

6.0 A/s

Answer

0 A/s

Answer

3.0 A/s

Answer

24 A/s

Question 13

A solid metal sphere carries a net charge +Q and is in electrostatic equilibrium. Which statement is true?

Accepted Answer

All of the excess charge is on the outer surface, and the electric field inside the metal is zero.

Answer

The excess charge is spread evenly through the volume, and the field inside is zero.

Answer

All of the excess charge is on the outer surface, and the field inside increases toward the surface.

Answer

The excess charge is spread evenly through the volume, and the field inside grows with distance from the center.

Question 14

A 2.0 kΩ resistor and a 50 μF capacitor are connected in series with a battery. What is the circuit’s time constant?

Accepted Answer

0.10 s

Answer

10 s

Answer

1.0 s

Answer

0.010 s

Question 15

A long, straight cylindrical wire of radius R carries a current spread uniformly over its cross section. The magnetic field at its surface is B₀. What is the field at a distance R/3 from the wire’s axis?

Accepted Answer

B₀/3

Answer

B₀/9

Answer

B₀

Answer

3B₀

Question 16

A +1.0 μC charge and a −1.0 μC charge are held 0.10 m apart. How much work must an outside agent do to pull them infinitely far apart, starting and ending at rest? (k = 9.0 × 10⁹ N·m²/C²)

Accepted Answer

+0.090 J

Answer

+0.90 J

Answer

0 J

Answer

−0.090 J

Question 17

A loop of area 0.20 m² lies perpendicular to a magnetic field that changes as B(t) = 0.50t², with B in teslas and t in seconds. What is the magnitude of the induced emf at t = 3.0 s?

Accepted Answer

0.60 V

Answer

0.30 V

Answer

0.90 V

Answer

3.0 V

Question 18

Resistors of 2.0 Ω and 4.0 Ω are connected in parallel across an ideal 8.0 V battery. What total power do they dissipate?

Accepted Answer

48 W

Answer

11 W

Answer

24 W

Answer

96 W

Question 19

Near a very large, flat, nonconducting sheet with a uniform surface charge, and far from its edges, how does the electric field depend on the distance from the sheet?

Accepted Answer

It has the same magnitude at every such distance.

Answer

It falls off as 1/r.

Answer

It falls off as 1/r².

Answer

It grows in proportion to the distance.

Question 20

An isolated, charged parallel-plate capacitor (not connected to anything) has a slab of dielectric with κ = 3 slid fully between its plates. What happens to the energy stored in the capacitor?

Accepted Answer

It drops to one third of its original value.

Answer

It triples.

Answer

It stays the same.

Answer

It drops to one ninth of its original value.

Question 21

Two long, straight, parallel wires carry currents in opposite directions. What force do the wires exert on each other?

Accepted Answer

They repel each other.

Answer

They attract each other.

Answer

They exert no force, because the currents cancel.

Answer

They push each other along the direction of the currents.

Question 22

At a point on an equipotential surface where the electric field is not zero, which statement about the field is true?

Accepted Answer

It is perpendicular to the surface and points toward lower potential.

Answer

It is perpendicular to the surface and points toward higher potential.

Answer

It is parallel to the surface.

Answer

Its direction depends on the sign of the test charge placed there.

Question 23

A 0.40 H inductor carries a steady current of 5.0 A. How much energy is stored in its magnetic field?

Accepted Answer

5.0 J

Answer

10 J

Answer

2.0 J

Answer

1.0 J

Question 24

A 12 V ideal battery is connected in series with a 4.0 Ω resistor, followed by an 8.0 Ω resistor that has a capacitor connected in parallel with it. Long after the circuit is connected, what is the voltage across the capacitor?

Accepted Answer

8.0 V

Answer

0 V

Answer

4.0 V

Answer

12 V

Question 25

A very long, straight line of charge produces an electric field of magnitude E at a distance r. What is the field at a distance 3r?

Accepted Answer

E/3

Answer

E/9

Answer

E/√3

Answer

E

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