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AP Physics C: Electricity and Magnetism Full-length practice exam 2

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Full-length practice exam 2

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Question 1

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 2

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 3

In the Wheatstone bridge circuit, resistors $R_{1}$ (top-left) and $R_{2}$ (top-right) form one pair of arms; $R_{3}$ (bottom-left) and $R_{X}$ (bottom-right) form the other. A galvanometer connects the midpoints. The bridge is balanced when:

R_{1} / R_{3} = R_{2} / R_{X}

R_{1} + R_{X} = R_{2} + R_{3}

R_{1} R_{2} = R_{3} R_{X}

R_{1} / R_{2} = R_{X} / R_{3}

Question 4

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 5

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 6

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 7

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 8

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 9

A circular loop of resistance $R = 5 Ω$ and radius $r = 0.10 m$ is pulled at constant velocity $v = 2 m/s$ out of a region of uniform magnetic field $B = 0.4 T$ (perpendicular to the loop). While the loop is partially out, the induced current is:

I_{ind} = B Lv / R

, where

L = 2 r = 0.20 m

is the chord in the field.B.

I_{ind} = B Lv / R

where

L

is the length of the loop edge cutting through the field boundary.C.

I_{ind} = B π r^{2} v / R

I_{ind} = 0

, because the flux is decreasing symmetrically.

Question 10

Three capacitors $C_{1} = 6 μ F$ , $C_{2} = 3 μ F$ , and $C_{3} = 2 μ F$ are connected in series across a $12 V$ battery. The total energy stored in the combination is:

72 μ J

648 μ J

144 μ J

36 μ J

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Question 11

An infinite plane of charge has surface charge density $σ$ . Using Gauss's law with a pillbox Gaussian surface that straddles the sheet, the electric field magnitude on each side of the sheet is:

E = \frac{σ}{ϵ _{0}}

E = \frac{σ}{2 ϵ _{0}}

E = \frac{2 σ}{ϵ _{0}}

E = \frac{σ}{4 π ϵ _{0}}

Question 12

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 13

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 14

A coaxial cylindrical capacitor has inner radius $a$ , outer radius $b$ , and length $L$ . The capacitance per unit length is:

C / L = \frac{2 π ϵ _{0}}{ln ( b / a )}

C / L = \frac{π ϵ _{0}}{ln ( b / a )}

C / L = \frac{2 π ϵ _{0} ( b - a )}{ab ln ( b / a )}

C / L = \frac{2 π ϵ _{0}}{b - a}

Question 15

An infinitely long line charge has linear charge density $λ > 0$ . Using Gauss's law with a coaxial cylindrical Gaussian surface of radius $r$ and length $L$ , the electric field at distance $r$ from the line is:

E = \frac{λ}{2 π ϵ _{0} r ^{2}}

E = \frac{λ}{2 π ϵ _{0} r}

E = \frac{λ L}{2 π ϵ _{0} r}

E = \frac{λ}{4 π ϵ _{0} r}

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Question 16

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 17

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 18

A conductor in electrostatic equilibrium has which of the following properties?

A.The electric field just outside the surface is

σ / ϵ_{0}

, directed perpendicular to the surface.B.The electric field inside the conductor is

σ / ϵ_{0}

.C.The electric potential varies parabolically throughout the conductor's volume.D.Excess charge distributes uniformly throughout the conductor's volume.

Question 19

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 20

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 21

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 22

A uniformly charged thin ring of radius $R$ and total charge $Q$ lies in the $x y$ -plane centered at the origin. The electric field on the axis of the ring at distance $z$ from the center points:

A.Radially outward from the ring's center, perpendicular to the axis.B.Along the

z

-axis (axial direction) for

z \neq = 0

.C.In the plane of the ring, toward the nearest point of the ring.D.Zero everywhere on the axis.

Question 23

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 24

A proton ( $m_{p} = 1.67 \times 1 0^{- 27} kg$ , $q = 1.60 \times 1 0^{- 19} C$ ) moving with speed $v = 2.0 \times 1 0^{6} m/s$ enters a region with both $E$ and $B$ fields. For the proton to travel in a straight line (velocity selector), with $v = v \overset{x}{^}$ , $B = B \overset{z}{^} = 0.050 T \overset{z}{^}$ , the required electric field $E$ and its magnitude are:

E = 1.0 \times 1 0^{5} V/m (- \overset{y}{^})

E = 1.0 \times 1 0^{5} V/m (+ \overset{y}{^})

E = 1.0 \times 1 0^{5} V/m (+ \overset{x}{^})

E = 4.0 \times 1 0^{- 14} V/m (+ \overset{y}{^})

Question 25

An RC circuit consists of a resistor $R = 200 k Ω$ and capacitor $C = 50 μ F$ connected in series with a battery $V_{0} = 10 V$ . The switch is closed at $t = 0$ with the capacitor initially uncharged. The voltage across the capacitor at time $t = τ = R C$ is:

V_{C} (τ) = V_{0} (1 - e^{- 1}) \approx 6.32 V

V_{C} (τ) = V_{0} / e \approx 3.68 V

V_{C} (τ) = V_{0} = 10 V

V_{C} (τ) = V_{0} /2 = 5 V

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Question 26

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.

Question 27

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 28

A parallel-plate capacitor (area $A$ , separation $d$ , no dielectric) is connected to a constant voltage source $V$ . A dielectric slab of thickness $t < d$ and dielectric constant $κ$ is inserted so that it fills the cross-section but only part of the gap. The capacitance of the resulting configuration is:

C = \frac{ϵ _{0} A}{d - t + t / κ}

C = \frac{κ ϵ _{0} A}{d}

C = \frac{ϵ _{0} A}{d + t ( κ - 1 )}

C = \frac{κ ϵ _{0} A}{d - t}

Question 29

Two long parallel wires separated by distance $d$ carry currents $I_{1}$ and $I_{2}$ in the same direction. The force per unit length between them is:

F / L = \frac{μ _{0} I _{1} I _{2}}{2 π d}

, attractive.B.

F / L = \frac{μ _{0} I _{1} I _{2}}{2 π d}

, repulsive.C.

F / L = \frac{μ _{0} I _{1} I _{2}}{4 π d}

, attractive.D.

F / L = \frac{μ _{0} I _{1} I _{2}}{π d ^{2}}

, repulsive.

Question 30

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

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Question 31

A proton ( $q = + e$ , $m_{p}$ ) moves with velocity $v = v \overset{x}{^}$ through a magnetic field $B = B \overset{z}{^}$ . The magnetic force on the proton is:

F = - e v B \overset{y}{^}

, directed in the

- y

direction.B.

F = + e v B \overset{y}{^}

, directed in the

+ y

direction.C.

F = + e v B \overset{z}{^}

, directed along the magnetic field.D.

F = 0

, because the proton moves perpendicular to the field.

Question 32

A solenoid of $N = 500$ turns, length $ℓ = 0.25 m$ , and cross-sectional area $A = 2.0 \times 1 0^{- 4} m^{2}$ carries current $I$ . The self-inductance of the solenoid is:

L = μ_{0} n^{2} A ℓ \approx 0.20 mH

L = μ_{0} N A / ℓ \approx 0.50 μ H

L = μ_{0} N^{2} / (A ℓ) \approx 1.26 \times 1 0^{9} H

L = μ_{0} N^{2} A \approx 6.28 \times 1 0^{- 5} H

Question 33

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

Question 34

An RC circuit with $R = 1 k Ω$ and $C = 10 μ F$ is driven by a square-wave voltage that steps from $0$ to $V_{0} = 10 V$ at $t = 0$ (with $C$ initially uncharged). The voltage across the capacitor at $t = 2 τ$ (where $τ = R C$ ) is:

V_{C} (2 τ) = V_{0} (1 - e^{- 2}) \approx 8.65 V

V_{C} (2 τ) = V_{0} (1 - e^{- 1/2}) \approx 3.94 V

V_{C} (2 τ) = 2 V_{0} (1 - e^{- 1}) \approx 12.6 V

V_{C} (2 τ) = V_{0} e^{- 2} \approx 1.35 V

Question 35

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.

AP Physics C: Electricity and Magnetism Full-length practice exam 2 — Free with Answer Explanations | Test Practice Hub