Deck 20: Electromagnetic Induction

Question 1

A conducting rod is free to slide on horizontal, frictionless rails separated by $2.0 \mathrm{~m}$ . At a particular time, the rod is sliding at $4.0 \mathrm{~m} / \mathrm{s}$ to the right, as shown. A uniform magnetic field is directed into the page. If a current of $40 \mathrm{~mA}$ is generated in the circuit at this time, and the resistance $\mathrm{R}$ is $0.36 \Omega$ , what is the magnitude of the magnetic field between the rails?

A) $0.028 \mathrm{~T}$
B) $1.8 \mathrm{mT}$
C) $0.11 \mathrm{~T}$
D) $3.6 \mathrm{mT}$
E) $14 \mathrm{mT}$

Answer 1

$1.8 \mathrm{mT}$

Question 2

The emf produced by an ac generator is given by $\varepsilon=\omega \mathrm{NBA} \sin \omega \mathrm{t}$ . In SI units, what is the value of $\omega$ for a frequency of $60.0 \mathrm{~Hz}$ ?

A) $60.0 \mathrm{~Hz}$
B) $377 \mathrm{~Hz}$
C) $2.00 \pi \mathrm{rad} / \mathrm{s}$
D) $120 \mathrm{rad} / \mathrm{s}$
E) $377 \mathrm{rad} / \mathrm{s}$

Answer 2

$377 \mathrm{rad} / \mathrm{s}$

Question 3

The SI unit $\mathrm{H}$ (the henry) is equal to a

A) $\mathrm{V} / \mathrm{m}$ .
B) $\mathrm{V} / \mathrm{A}$ .
C) V.s/A.
D) $\mathrm{V} \cdot \mathrm{s}$ .
E) $\mathrm{V} \cdot \mathrm{A} / \mathrm{s}$

Answer 3

V.s/A.

Question 4

The unit of magnetic flux is the weber. $1 \mathrm{~Wb}$ equals

A) $1 \mathrm{~V} \cdot \mathrm{s} / \mathrm{A}$ .
B) $1 \mathrm{~V} \cdot \mathrm{m}$ .
C) $1 \mathrm{~T} \cdot \mathrm{m}^{2}$ .
D) $\pi$ lines $/ \mathrm{m}^{2}$ .

Question 5

A flat coil has a maximum flux of $4.0 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2}$ through it, with its area perpendicular to a uniform magnetic field. When the coil is rotated $60^{\circ}$ (so that its normal makes a $60^{\circ}$ angle with the field), what is the flux through it?

A) $3.5 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2}$
B) $6.9 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2}$
C) $2.0 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2}$
D) $4.0 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2}$
E) $8.0 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2}$

Question 6

A hollow copper pipe is held vertically, and a magnet is dropped down the pipe. The magnet is oriented with its north pole down. What direction do the eddy currents flow as viewed from above the pipe? If copper bar of approximately the same size and weight as the magnet is dropped down the tube instead, will it fall faster or slower than the magnet?

A) CCW above the magnet and CW below the magnet; copper bar will fall slower
B) $\mathrm{CW}$ above the magnet and $\mathrm{CCW}$ below the magnet; copper bar will fall faster
C) $\mathrm{CCW}$ above the magnet and $\mathrm{CW}$ below the magnet; copper bar will fall faster
D) $\mathrm{CW}$ above the magnet and CCW below the magnet; copper bar will fall slower

Question 7

A solenoid of length $4.00 \mathrm{~cm}$ and cross-sectional area $2.00 \mathrm{~cm}^{2}$ has 80 turns. What is its self-inductance?

A) $120 \mu \mathrm{H}$
B) $40.2 \mu \mathrm{H}$
C) $80.0 \mu \mathrm{H}$
D) $160 \mu \mathrm{H}$
E) $0.500 \mu \mathrm{H}$

Question 8

If the magnetic energy stored by a $0.50 \mathrm{H}$ inductor is $3.6 \mathrm{~J}$ , what is the current through it?

A) $0.90 \mathrm{~A}$
B) $5.4 \mathrm{~A}$
C) $0.13 \mathrm{~A}$
D) $1.8 \mathrm{~A}$
E) $3.8 \mathrm{~A}$

Question 9

What is the magnetic energy stored by a $300 \mathrm{mH}$ inductor with a 2.0 A current going through it?

A) $1.2 \mathrm{~J}$
B) $0.60 \mathrm{~J}$
C) $30 \mathrm{~mJ}$
D) $0.075 \mathrm{~J}$
E) $0.15 \mathrm{~J}$

Question 10

The current in a $0.40 \mathrm{H}$ inductor increases form $2.0 \mathrm{~A}$ to $3.0 \mathrm{~A}$ in $1.5 \mathrm{~s}$ . The energy stored by the inductor during this process increases by

A) $1.8 \mathrm{~J}$ .
B) $3.6 \mathrm{~J}$ .
C) $1.0 \mathrm{~J}$ .
D) $0.6 \mathrm{~J}$ .
E) $1.2 \mathrm{~J}$ .

Question 11

What is the magnetic energy density in a volume where the magnetic field is $4.0 \mathrm{mT}$ ?

A) $3.2 \times 10^{-3} \mathrm{~J} / \mathrm{m}^{3}$
B) $13 \times 10^{-3} \mathrm{~J} / \mathrm{m}^{3}$
C) $6.4 \mathrm{~J} / \mathrm{m}^{3}$
D) $3.2 \mathrm{~J} / \mathrm{m}^{3}$
E) $13 \mathrm{~J} / \mathrm{m}^{3}$

Question 12

A $0.40 \mathrm{H}$ inductor has a current that rises from zero to $3.0 \mathrm{~A}$ in $6.0 \mathrm{~s}$ . What is the average power required to accomplish this?

A) $1.5 \mathrm{~W}$
B) $0.60 \mathrm{~W}$
C) $9.0 \mathrm{~W}$
D) $15 \mathrm{~W}$
E) $0.30 \mathrm{~W}$

Question 13

What electric field has the same energy density as a $1.0 \mathrm{~T}$ magnetic field?

A) $1.1 \times 10-17 \mathrm{~V} / \mathrm{m}$
B) $9.0 \times 1016 \mathrm{~V} / \mathrm{m}$
C) $1.0 \mathrm{~V} / \mathrm{m}$
D) $3.0 \times 10^{8} \mathrm{~V} / \mathrm{m}$
E) $3.3 \times 10-9 \mathrm{~V} / \mathrm{m}$

Question 14

A series LR circuit includes a $9.00 \mathrm{~V}$ battery, a $30.0 \mathrm{mH}$ inductor, and a resistance of $5.00 \Omega$ . What is the time constant of this circuit?

A) $170 \mathrm{~s}$
B) $115 \mathrm{~s}$
C) $4.20 \mathrm{~ms}$
D) $8.30 \mathrm{~ms}$
E) $6.00 \mathrm{~ms}$

Question 15

A series LR circuit includes a $9.0 \mathrm{~V}$ battery, a resistance of $0.50 \Omega$ , and an inductance of $0.80 \mathrm{H}$ . What is the current 2.0 s after the switch is closed?

A) $13 \mathrm{~A}$
B) $6.4 \mathrm{~A}$
C) $4.3 \mathrm{~A}$
D) $18 \mathrm{~A}$
E) $5.2 \mathrm{~A}$

Question 16

A series LR circuit includes a $9.0 \mathrm{~V}$ battery, a resistance of $0.50 \Omega$ , and an inductance of $0.80 \mathrm{H}$ . What is the induced emf $2.0 \mathrm{~s}$ after the switch has been closed?

A) 0.0
B) $19 \mathrm{mV}$
C) $9.0 \mathrm{~V}$
D) $2.6 \mathrm{~V}$
E) $5.2 \mathrm{~V}$

Question 17

A series LR circuit includes a $9.0 \mathrm{~V}$ battery, a resistance of $0.50 \Omega$ , and an inductance of $0.80 \mathrm{H}$ . What is the energy stored by the inductor $2.0 \mathrm{~s}$ after the switch is closed?

A) $13 \mathrm{~J}$
B) $33 \mathrm{~mJ}$
C) $66 \mathrm{~J}$
D) $30 \mathrm{~mJ}$
E) $33 \mathrm{~J}$

Question 18

A series LR circuit includes a $9.00 \mathrm{~V}$ battery, a resistance of $0.500 \Omega$ , and an inductance of $0.800 \mathrm{H}$ . What is the greatest energy stored by the inductor after the switch is closed?

A) $33.0 \mathrm{~mJ}$
B) $65.0 \mathrm{~J}$
C) $130 \mathrm{~J}$
D) $33.0 \mathrm{~J}$
E) $13.0 \mathrm{~mJ}$

Question 19

A square conducting loop is situated such that it is vertical, in the xz-plane. The Earth's gravitational field points downward (in the $-\mathrm{z}$ direction). The loop is dropped and maintains its orientation in the xz-plane. A magnetic field pointing in the $+y$ direction exists and is uniform with respect to time, but it varies as a function of $\mathrm{z}: \mathrm{B}_{\mathrm{y}}(\mathrm{z})=\mathrm{B}_{0}(10 \mathrm{~m}-\mathrm{z})$ . The loop is dropped and allowed to fall under the influence of gravitation. You observe the loop from the $+y$ direction (i.e., looking toward the $-y$ direction). Which of the following occurs?

A) The situation is unclear because we do not know the initial conditions.
B) There is a counter-clockwise induced current.
C) There is a clockwise induced current.
D) There is no induced current.

Question 20

A horse and rider travel in a region in which the vertical component of the Earth's magnetic field is $0.035 \mathrm{mT}$ , while the horizontal component is $0.022 \mathrm{mT}$ . Attached to the horse's bridle is a metal bit, a horizontal cylinder approximately $15 \mathrm{~cm}$ long, in the horse's mouth. If the horse is galloping at $15 \mathrm{~m} / \mathrm{s}$ , what is the induced potential difference between the ends of the bit?

A) $50 \mu \mathrm{V}$
B) $93 \mathrm{mV}$
C) $79 \mu \mathrm{V}$
D) $79 \mathrm{mV}$
E) $93 \mu \mathrm{V}$
F) $50 \mathrm{mV}$