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AP Physics C: Electricity and Magnetism Full-length practice exam 1 — Free with Answer Explanations | Test Practice Hub

AP Physics C: Electricity and Magnetism Full-length practice exam 1

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Full-length practice exam 1

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Question 1

Two large parallel conducting plates separated by distance $d$ each carry surface charge density $+ σ$ and $- σ$ respectively. A small conducting sphere of radius $a ≪ d$ with net charge $q$ is held midway between the plates. Ignoring image charges, the electric force on the sphere is:

F = q σ / ϵ_{0}

, directed from the positive to the negative plate.B.

F = q σ / (2 ϵ_{0})

, directed from the positive to the negative plate.C.

F = 0

, because the sphere is midway between the plates.D.

F = 2 q σ / ϵ_{0}

, directed from the positive to the negative plate.

Question 2

An ammeter has negligible resistance. A voltmeter has very high resistance. Which connection correctly measures the voltage across resistor $R_{2}$ in a series circuit containing $R_{1}$ and $R_{2}$ ?

A.Connect the voltmeter in parallel with

R_{2}

and the ammeter in series in the branch containing

R_{2}

.B.Connect both the voltmeter and ammeter in series with

R_{2}

.C.Connect the voltmeter in series with

R_{2}

and the ammeter in parallel with

R_{2}

.D.Connect both the voltmeter and ammeter in parallel with

R_{2}

Question 3

A solid insulating cylinder of radius $R$ and infinite length has non-uniform volume charge density $ρ (r) = ρ_{0} r / R$ , where $r$ is the distance from the axis. Using Gauss's law, the electric field magnitude for $r < R$ is:

E = \frac{ρ _{0} r ^{2}}{3 ϵ _{0} R}

E = \frac{ρ _{0} r}{3 ϵ _{0}}

E = \frac{ρ _{0} r ^{2}}{2 ϵ _{0} R}

E = \frac{ρ _{0} R}{3 ϵ _{0}}

Question 4

A spherical conducting shell of inner radius $a$ and outer radius $b$ carries a net charge $+ Q$ . A point charge $+ q$ is placed at the center. By Gauss's law, the surface charge density on the outer surface of the shell is:

σ_{outer} = \frac{Q}{4 π b ^{2}}

σ_{outer} = \frac{Q + q}{4 π b ^{2}}

σ_{outer} = \frac{Q - q}{4 π b ^{2}}

σ_{outer} = \frac{q}{4 π b ^{2}}

Question 5

A long straight wire carries current $I = 5 A$ . The magnetic field at a perpendicular distance $r = 0.10 m$ from the wire has magnitude (using $μ_{0} = 4 π \times 1 0^{- 7} T\cdotm/A$ ):

B = 10 μ T

B = 100 μ T

B = 1 μ T

B = 50 μ T

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Question 6

An RL circuit ( $R = 20 Ω$ , $L = 0.40 H$ ) is powered by $E = 10 V$ . After a long time the switch is opened. The current through the inductor at time $t$ after opening is:

I (t) = I_{0} e^{- R t / L} = 0.50 e^{- 50 t} A

I (t) = I_{0} (1 - e^{- R t / L})

I (t) = I_{0} e^{- t / R C}

(RC decay formula)D.

I (t) = 0

immediately after the switch opens.

Question 7

A solenoid of length $L = 0.50 m$ , $N = 1000$ turns, and radius $r ≪ L$ carries current $I = 2 A$ . Using Ampère's law, the magnetic field inside the solenoid is:

B = μ_{0} n I \approx 5.0 mT

B = μ_{0} N I / (2 π r)

B = μ_{0} N I / L^{2}

B = μ_{0} I / (2 π r)

Question 8

Using the Biot-Savart law, the magnetic field at the center of a circular loop of radius $R$ carrying current $I$ is:

B = \frac{μ _{0} I}{2 R}

B = \frac{μ _{0} I}{4 π R}

B = \frac{μ _{0} I}{2 π R}

B = \frac{μ _{0} I R ^{2}}{2 ( R ^{2} + R ^{2} ) ^{3/2}}

Question 9

A rectangular loop of area $A = 0.04 m^{2}$ is in a uniform magnetic field $B$ that increases at rate $d B / d t = 50 T/s$ . The magnitude of the induced EMF in the loop is:

E = 2.0 V

E = 0.04 V

E = 50 V

E = 1250 V

Question 10

A transformer has primary coil $N_{1} = 200$ turns and secondary coil $N_{2} = 50$ turns. The primary is connected to $V_{1} = 120 V$ (rms) AC. A load $R_{L} = 10 Ω$ is connected to the secondary. Assuming an ideal transformer (no losses), the primary current $I_{1}$ (rms) is:

I_{1} = 0.75 A

I_{1} = 12 A

I_{1} = 3.0 A

I_{1} = 0.60 A

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Question 11

In the circuit below, $E_{1} = 12 V$ , $E_{2} = 6 V$ , $R_{1} = 4 Ω$ , and $R_{2} = 2 Ω$ . The two batteries and resistors are in a single loop, with $E_{1}$ and $E_{2}$ opposing each other. Applying Kirchhoff's voltage law, the current (taking $E_{1}$ 's direction as positive) is:

I = 1 A

I = 3 A

I = - 1 A

I = 2 A

Question 12

Two capacitors $C_{1} = 4 μ F$ (initially charged to $V_{1} = 12 V$ ) and $C_{2} = 8 μ F$ (initially uncharged) are connected in parallel by closing a switch. The final common voltage and the energy dissipated in the connecting wires are:

V_{f} = 4 V

;

Δ U_{dissipated} = 192 μ J

V_{f} = 6 V

;

Δ U_{dissipated} = 144 μ J

V_{f} = 4 V

;

Δ U_{dissipated} = 0

V_{f} = 12 V

;

Δ U_{dissipated} = 576 μ J

Question 13

An LC circuit consists of an inductor $L = 0.10 H$ and capacitor $C = 100 μ F$ . The capacitor is initially charged to $V_{0} = 10 V$ and the switch is closed at $t = 0$ . The angular frequency of oscillation $ω$ and the maximum current $I_{m a x}$ are:

ω = 1/ L C \approx 316 rad/s

;

I_{m a x} = V_{0} C / L \approx 0.316 A

ω = 1/ L C \approx 316 rad/s

;

I_{m a x} = V_{0} / R =

undefined (no

R

)C.

ω = L C \approx 0.00316 rad/s

;

I_{m a x} = V_{0} / L C \approx 3162 A

ω = 1/ (L C) \approx 1 0^{5} rad/s

;

I_{m a x} = C V_{0} ω =

incorrect

Question 14

A finite line segment of length $2 L$ lies along the $x$ -axis, centered at the origin, with uniform linear charge density $λ$ . What is the electric potential $V$ at a point $P$ on the perpendicular bisector (the $y$ -axis) at distance $d$ from the origin?

V = \frac{λ}{2 π ϵ _{0}} ln (\frac{L + L ^{2} + d ^{2}}{d})

V = \frac{λ L}{2 π ϵ _{0} d}

V = \frac{λ}{4 π ϵ _{0}} ln (\frac{L + d}{L - d})

V = \frac{λ}{2 π ϵ _{0}} ln (\frac{d}{L + L ^{2} + d ^{2}})

Question 15

Lenz's law states that the direction of the induced current in a loop is such that:

A.The induced current's magnetic field opposes the change in flux that caused it.B.The induced current's magnetic field reinforces the change in flux, amplifying the effect.C.The induced current always flows clockwise when viewed from above.D.The induced EMF is proportional to the magnetic flux, not its rate of change.

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Question 16

A conducting rod of length $L = 0.50 m$ moves with velocity $v = 4 m/s$ perpendicular to a uniform magnetic field $B = 0.30 T$ . The motional EMF induced in the rod is:

E = B Lv = 0.60 V

E = B L / v = 0.0375 V

E = B / Lv = 0.15 V

E = B L^{2} v = 0.30 V

Question 17

A charged isolated conductor has a sharp point (small radius of curvature $r$ ) and a flat region (large radius of curvature). Which statement correctly describes the charge distribution?

A.Surface charge density and electric field are highest at the sharp point.B.Surface charge density is uniform across the entire conductor surface.C.The electric field is stronger over flat regions because there is more area for charge to spread.D.Electric field inside the conductor is largest near the sharp point.

Question 18

A capacitor of capacitance $C$ is fully charged to voltage $V_{0}$ and then disconnected from the battery. A dielectric of dielectric constant $κ$ is then inserted, filling the gap completely. What happens to the stored energy?

A.The energy decreases by a factor of

κ

.B.The energy increases by a factor of

κ

.C.The energy remains the same, because charge is conserved.D.The energy increases by a factor of

κ^{2}

Question 19

A parallel-plate capacitor has plate area $A$ and plate separation $d$ . The capacitance is:

C = \frac{ϵ _{0} A}{d}

C = \frac{ϵ _{0} d}{A}

C = \frac{A}{4 π ϵ _{0} d}

C = \frac{ϵ _{0} A}{2 d}

Question 20

A toroid has $N$ turns, inner radius $a$ , outer radius $b$ , and carries current $I$ . Using Ampère's law with a circular Amperean loop of radius $r$ ( $a < r < b$ ), the magnetic field inside the toroid is:

B = \frac{μ _{0} N I}{2 π r}

B = μ_{0} n I

where

n = N / (2 π r)

, same as a straight solenoid.C.

B = \frac{μ _{0} N I}{2 π a}

(uniform inside the toroid).D.

B = 0

inside the toroid.

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Question 21

A rectangular current loop ( $a \times b$ ) carrying current $I$ is placed in a uniform magnetic field $B$ with its plane parallel to $B$ (the normal to the loop is perpendicular to $B$ ). The torque on the loop is:

τ = I A B

τ = 0

τ = 2 I A B

τ = I A^{2} B / a

Question 22

Two point charges $q_{1} = + 3 μ C$ and $q_{2} = - 3 μ C$ are separated by $r = 0.30 m$ . Using $k = 9 \times 1 0^{9} N\cdotm^{2} / C^{2}$ , the magnitude of the electric force between them is:

0.90 N

0.30 N

0.10 N

8.1 \times 1 0^{- 3} N

Question 23

A resistor $R = 10 Ω$ is connected to a battery of EMF $E = 20 V$ and internal resistance $r = 2 Ω$ . The current through the circuit is:

I = 2 A

I = 5/3 A \approx 1.67 A

I = 10 A

I = 1 A

Question 24

A Hall-effect sensor: a flat conductor (width $w$ , thickness $t$ ) carries current $I$ in the $+ x$ direction in a field $B = B \overset{z}{^}$ . Charge carriers are electrons (charge $- e$ , number density $n$ ). At steady state, the magnitude of the Hall voltage across width $w$ is:

V_{H} = \frac{I B}{n e t}

V_{H} = \frac{I B}{2 n e t}

V_{H} = 0

, because the magnetic force on electrons and ions cancels.D.

V_{H} = \frac{I B}{2 n e t}

(split evenly between edges).

Question 25

Three resistors $R_{1} = 2 Ω$ , $R_{2} = 3 Ω$ , $R_{3} = 6 Ω$ are connected in parallel across a $12 V$ source. The total power delivered by the source is:

P = 132 W

P = 144 W

P = 16 W

P = 72 W

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Question 26

A parallel-plate capacitor with plate area $A = 0.10 m^{2}$ and gap $d = 2 mm$ is filled with a dielectric of $κ = 5$ . A voltage $V = 100 V$ is applied. The surface charge density $σ_{f}$ on the capacitor plates (free charge) is:

σ_{f} = κ ϵ_{0} V / d \approx 2.21 μ C/m^{2}

σ_{f} = ϵ_{0} V / d \approx 0.44 μ C/m^{2}

σ_{f} = ϵ_{0} V / (κ d) \approx 0.089 μ C/m^{2}

σ_{f} = κ^{2} ϵ_{0} V / d \approx 11.1 μ C/m^{2}

Question 27

Using the Biot-Savart law, the magnetic field at a point $P$ on the axis of a circular loop of radius $R$ at axial distance $z$ from the center is:

B = \frac{μ _{0} I R ^{2}}{2 ( R ^{2} + z ^{2} ) ^{3/2}}

B = \frac{μ _{0} I}{2 R ^{2} + z ^{2}}

B = \frac{μ _{0} I R}{2 ( R ^{2} + z ^{2} )}

B = \frac{μ _{0} I}{2 R}

(same as at the center, independent of

z

Question 28

Two coils have mutual inductance $M = 0.020 H$ . Coil 1 carries a current that changes at rate $d I_{1} / d t = 30 A/s$ . The magnitude of the EMF induced in coil 2 is:

∣ E_{2} ∣ = M ∣ d I_{1} / d t ∣ = 0.60 V

∣ E_{2} ∣ = M ∣ I_{1} ∣ =

unknown (need

I_{1}

, not

d I_{1} / d t

).C.

∣ E_{2} ∣ = M^{2} ∣ d I_{1} / d t ∣ = 0.012 V

∣ E_{2} ∣ = (d I_{1} / d t) / M = 1500 V

Question 29

The energy stored in an inductor of inductance $L = 50 mH$ carrying current $I = 4 A$ is:

U_{L} = \frac{1}{2} L I^{2} = 0.40 J

U_{L} = L I^{2} = 0.80 J

U_{L} = \frac{L}{2 I ^{2}} = 0.0016 J

U_{L} = \frac{1}{2} \frac{I ^{2}}{L} = 160 J

Question 30

A solid insulating sphere of radius $R$ carries uniform volume charge density $ρ$ . For a point inside the sphere at radius $r < R$ , Gauss's law gives the electric field magnitude:

E = \frac{ρ R ^{3}}{3 ϵ _{0} r ^{2}}

E = \frac{ρ r}{3 ϵ _{0}}

E = \frac{ρR}{3 ϵ _{0}}

E = 0

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Question 31

An RC circuit has $R = 10 k Ω$ , $C = 20 μ F$ , and battery $V_{0} = 6 V$ . The switch is closed at $t = 0$ with $C$ initially uncharged. The energy dissipated in the resistor from $t = 0$ to $t \to \infty$ is:

E_{R} = \frac{1}{2} C V_{0}^{2} = 360 μ J

E_{R} = C V_{0}^{2} = 720 μ J

E_{R} = \frac{V _{0}^{2}}{2 R} = 1.8 \times 1 0^{- 3} J

E_{R} = 0

, because an ideal resistor stores no energy.

Question 32

Using Ampère's law, the magnetic field at a distance $r$ inside a long cylindrical conductor of radius $R$ carrying a total current $I$ uniformly distributed over its cross section is:

B = \frac{μ _{0} I r}{2 π R ^{2}}

for

r < R

B = \frac{μ _{0} I}{2 π r}

for

r < R

B = 0

for

r < R

B = \frac{μ _{0} I}{2 π R ^{2}}

for

r < R

Question 33

The energy density stored in the electric field of a parallel-plate capacitor filled with dielectric $κ$ and field $E$ is:

u = \frac{1}{2} κ ϵ_{0} E^{2}

u = \frac{1}{2} ϵ_{0} E^{2}

u = \frac{1}{2 κ ϵ _{0} E ^{2}}

u = κ ϵ_{0} E^{2}

Question 34

An RL circuit has $R = 50 Ω$ , $L = 0.10 H$ , and battery $E = 20 V$ . The switch is closed at $t = 0$ . The current as a function of time is $I (t) = I_{m a x} (1 - e^{- t / τ_{L}})$ with $τ_{L} = L / R$ . The initial rate of change of current $d I / d t ∣_{t = 0}$ is:

d I / d t ∣_{t = 0} = E / L = 200 A/s

d I / d t ∣_{t = 0} = E / R = 0.40 A/s

d I / d t ∣_{t = 0} = 0

d I / d t ∣_{t = 0} = E / (R L) = 4 A/s

Question 35

In a circuit with two parallel resistors $R_{1} = 6 Ω$ and $R_{2} = 3 Ω$ in series with $R_{3} = 4 Ω$ , connected to a $12 V$ ideal battery, the voltage across the parallel combination is:

V_{∥} = 4 V

V_{∥} = 6 V

V_{∥} = 8 V

V_{∥} = 12 V