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AP Physics C: Electricity and Magnetism Unit 4: Magnetic Fields

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Unit 4: Magnetic Fields

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Question 1

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 2

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 3

A particle of mass $m$ , charge $q$ , enters a uniform magnetic field $B$ perpendicular to its velocity $v$ . The radius of the circular orbit is:

r = \frac{m v}{q B}

r = \frac{q B}{m v}

r = \frac{m v ^{2}}{q B}

r = \frac{m}{q v B}

Question 4

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 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

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 7

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 8

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 9

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 10

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.

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Question 11

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 12

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

AP Physics C: Electricity and Magnetism Unit 4: Magnetic Fields — Free with Answer Explanations | Test Practice Hub