Pearson Physics

James S. Walker

Chapter 23

Electromagnetic Induction - all with Video Answers

Educators

+ 6 more educators

Chapter Questions

Problem 1

At what angle is the flux equal to $1.00 \times 10^{-4} \mathrm{~T} \cdot \mathrm{m}^{2}$ ?

Rashmi Sinha

Rashmi Sinha

Numerade Educator

Problem 2

The magnetic flux through a circular loop is $4.6 \times 10^{-4} \mathrm{~T} \cdot \mathrm{m}^{2}$. If the normal to the loop makes an angle of $45^{\circ}$ with a magnetic field of $0.50 \mathrm{~T}$, what is the area of the loop?

Prabhat Tyagi

Numerade Educator

Problem 3

A rectangular loop $3.2 \mathrm{~cm}$ wide and $5.1 \mathrm{~cm}$ long is placed in a magnetic field. The angle between the normal to the loop and the magnetic field is $32^{\circ}$, and the magnetic flux through the loop is $2.2 \times 10^{-3} \mathrm{~T} \cdot \mathrm{m}^{2}$. What is the magnitude of the magnetic field?

Supratim Pal

Numerade Educator

Problem 4

Follow-up How many loops of wire are needed in the coil to give an induced emf of $1.5 \mathrm{~V}$ ?

Rashmi Sinha

Numerade Educator

Problem 5

A 15-loop coil experiences an induced emf of $0.78 \mathrm{~V}$ when the magnetic flux is changed in $0.45 \mathrm{~s}$. What is the change in magnetic flux?

Prabhat Tyagi

Numerade Educator

Problem 6

The magnetic flux through a 25-loop wire coil changes by $2.6 \times 10^{-4} \mathrm{~T} \cdot \mathrm{m}^{2}$ and produces an induced emf of $1.7 \mathrm{~V}$. How much time is required for this change in magnetic flux?

Prabhat Tyagi

Numerade Educator

Problem 7

What produces a larger induced emf, a magnetic field that changes quickly or slowly?

Supratim Pal

Numerade Educator

Problem 8

How does the magnetic flux change when the area of a wire loop is doubled and the magnetic field is halved?

Narayan Hari

Numerade Educator

Problem 9

How is Lenz's law related to the direction of an induced current?

Supratim Pal

Numerade Educator

Problem 10

Do constant magnetic fields produce electric fields? Do changing magnetic fields produce electric fields?

Supratim Pal

Numerade Educator

Problem 11

Two identical wire loops have magnetic fields of equal magnitude but different directions. The magnetic field for loop 1 has an angle of $10^{\circ}$ with the normal to that loop, and the magnetic field for loop 2 has an angle of $20^{\circ}$ with the loop's normal. Is the magnetic flux for loop 1 greater than, less than, or equal to the magnetic flux for loop 2? Explain.

Dominador Tan

Numerade Educator

Problem 12

Triple Choice A region of space has a magnetic field that points out of the page. The field is uniform in the $y$ direction, but increases in strength in the positive $x$ direction, as indicated in Figure 23. 10. Four wire loops move through the region in different directions. For each of the loops, state whether its induced current is clockwise, counterclockwise, or zero.

Gregory Devenport

Gregory Devenport

Numerade Educator

Problem 13

A rectangular wire loop $32 \mathrm{~cm}$ long and $16 \mathrm{~cm}$ wide is placed in a magnetic field with a magnitude of $0.77 \mathrm{~T}$. The magnetic field is either (a) perpendicular to the plane of the loop or (b) parallel to the plane of the loop. Calculate the magnetic flux for each of these cases.

Supratim Pal

Numerade Educator

Problem 14

The induced emf in a single loop of wire has a magnitude of $1.48 \mathrm{~V}$ when the magnetic flux is changed from $0.850 \mathrm{~T} \cdot \mathrm{m}^{2}$ to $0.110 \mathrm{~T} \cdot \mathrm{m}^{2}$. How much time is required for this change in flux?

Hubert Agamasu

Numerade Educator

Problem 15

The magnetic flux on a 25-loop wire coil is changed in $0.35 \mathrm{~s}$. The result is an induced emf of $2.6 \mathrm{~V}$. What was the magnitude of the change in magnetic flux?

Prabhat Tyagi

Numerade Educator

Problem 16

What is the angle between the normal to a wire loop and the magnetic field, given that the magnitude of the field is $0.45 \mathrm{~T}$, the area of the loop is $0.085 \mathrm{~m}^{2}$, and the magnetic flux is $7.1 \times 10^{-4} \mathrm{~T} \cdot \mathrm{m}^{2}$ ?

Supratim Pal

Numerade Educator

Problem 17

Follow-up What is the maximum emf of the generator in Guided Example $23.6$ if its rotational frequency is reduced to $50.0 \mathrm{~Hz}$ ? (Recall that angular speed, $\omega$, is related to rotational frequency, $f$, by $\omega=2 \pi f .$ )

Supratim Pal

Numerade Educator

Problem 18

What is the minimum number of loops required for a coil of area $5.1 \times 10^{-3} \mathrm{~m}^{2}$ and angular speed $350 \mathrm{rad} / \mathrm{s}$ to produce a maximum emf of $95 \mathrm{~V}$ in a magnetic field of strength $1.5 \mathrm{~T}$ ?

Prabhat Tyagi

Numerade Educator

Problem 19

A 45-loop coil produces a maximum emf of $65 \mathrm{~V}$ as it rotates with an angular speed of $250 \mathrm{rad} / \mathrm{s}$ in a magnetic field with a strength of $2.0 \mathrm{~T}$. What is the area of the coil?

Vishal Gupta

Numerade Educator

Problem 20

What is the power source for an electric generator?

Prabhat Tyagi

Numerade Educator

Problem 21

In what ways are electric motors and electric generators different? In what ways are they similar?

Supratim Pal

Numerade Educator

Problem 22

If the angular speed of a generator is increased, does the maximum emf produced by the generator increase, decrease, or stay the same? Explain.

Vishal Gupta

Numerade Educator

Problem 23

If the number of loops of a generator coil is increased, does the maximum emf produced by the generator increase, decrease, or stay the same? Explain.

Vishal Gupta

Numerade Educator

Problem 24

A 95-loop generator coil produces a maximum emf of $75 \mathrm{~V}$ when it rotates with an angular speed of $220 \mathrm{rad} / \mathrm{s}$. If the area of the coil's loops is $0.0044 \mathrm{~m}^{2}$, what is the magnitude of the magnetic field?

Vishal Gupta

Numerade Educator

Problem 25

A generator has a 55-loop coil with an area of $0.0085 \mathrm{~m}^{2}$. If the coil rotates with an angular speed of $310 \mathrm{rad} / \mathrm{s}$ in a magnetic field with a magnitude of $0.95 \mathrm{~T}$, what is the maximum emf?

Vishal Gupta

Numerade Educator

Problem 26

What area must a 27-loop coil have if it is to produce a maximum emf of $22 \mathrm{~V}$ when rotating in a magnetic field of $0.82 \mathrm{~T}$ with an angular speed of $290 \mathrm{rad} / \mathrm{s}$ ?

Vishal Gupta

Numerade Educator

Problem 27

An AC circuit has a current whose maximum value is $2.7 \mathrm{~A}$. What is the rms current in this circuit?

Vishal Gupta

Numerade Educator

Problem 28

What is the maximum current in an $\mathrm{AC}$ circuit that has an rms current of $1.6 \mathrm{~A}$ ?

Vishal Gupta

Numerade Educator

Problem 29

Suppose we would like the average power dissipated in the resistor to be $5.00 \mathrm{~W}$. Should the resistance be increased or decreased, assuming that the same $\mathrm{AC}$ generator is used? Find the required value of $R$.

Vishal Gupta

Numerade Educator

Problem 30

An AC generator with a frequency of $60.0 \mathrm{~Hz}$ is connected to a 375- $\Omega$ resistor. If the average power dissipated in the resistor is $2.25 \mathrm{~W}$, what is the maximum voltage of the generator?

Vishal Gupta

Numerade Educator

Problem 31

What is the maximum current in an AC circuit that contains a 232- $\Omega$ resistor and dissipates an average power of $4.45 \mathrm{~W} ?$

Vishal Gupta

Numerade Educator

Problem 32

What trigonometric function describes how voltage and current vary with time in an AC circuit?

Supratim Pal

Numerade Educator

Problem 33

What change must be made to the DC power formula, $P=I^{2} R$, for it to apply to the average power of an $\mathrm{AC}$ circuit?

Prabhat Tyagi

Numerade Educator

Problem 34

A transformer has more loops on its secondary coil than it has on its primary coil. What effect does the transformer have on voltage?

Vishal Gupta

Numerade Educator

Problem 35

If a transformer increases the voltage in a circuit, what happens to the current?

Vishal Gupta

Numerade Educator

Problem 36

What is the advantage of an rms value in analyzing an $\mathrm{AC}$ circuit?

Supratim Pal

Numerade Educator

Problem 37

A transformer has twice the number of loops on its secondary coil as on its primary coil.
(a) What is the ratio of the secondary voltage to the primary voltage?
(b) What is the ratio of the secondary current to the primary current?

Vishal Gupta

Numerade Educator

Problem 38

The rms current in a circuit is $2.5 \mathrm{~A}$. What is the maximum current in the circuit?

Vishal Gupta

Numerade Educator

Problem 39

An AC circuit has a maximum voltage of $5.0 \mathrm{~V}$. What is the rms voltage of this circuit?

Vishal Gupta

Numerade Educator

Problem 40

An AC circuit has an rms current of
$3.2 \mathrm{~A}$. What is the average power dissipated in a $180-\Omega$ resistor?

Vishal Gupta

Numerade Educator

Problem 41

A transformer has 50 loops in the primary coil and 125 loops in the secondary coil.
The voltage in the primary circuit is $25 \mathrm{~V}$.
(a) Is the voltage in the secondary circuit greater than, less than, or equal to $25 \mathrm{~V}$ ?
(b) What is the voltage in the secondary circuit?

Vishal Gupta

Numerade Educator

Problem 42

A transformer has 150 loops in the primary coil and 35 loops in the secondary coil. The current in the primary circuit is $2.1 \mathrm{~A}$.
(a) Is the current in the secondary circuit greater than, less than, or equal to $2.1 \mathrm{~A}$ ?
(b) What is the current in the secondary circuit?

Supratim Pal

Numerade Educator

Problem 43

Explain the difference between a magnetic field and a magnetic flux.

Vishal Gupta

Numerade Educator

Problem 44

A metal ring with a break in it is dropped from a fieldfree region of space into a region with a magnetic field. What effect does the magnetic field have on the ring?

Vishal Gupta

Numerade Educator

Problem 45

In a common classroom demonstration, a magnet is dropped down a long, vertical copper tube. The magnet moves very slowly as it falls through the tube, taking several seconds to reach the bottom. Explain this behavior.

Vishal Gupta

Numerade Educator

Problem 46

Many equal-arm balances have a small metal plate attached to one of the two arms. The plate passes between the poles of a magnet mounted in the base of the balance. Explain the purpose of this arrangement.

Vishal Gupta

Numerade Educator

Problem 47

Figure 23.21 shows a vertical iron rod with a wire coil of many loops wrapped around its base. A metal ring slides over the rod and rests on the wire coil. Initially, the switch connecting the coil to a battery is open, but when it is closed, the ring flies into the air. Explain why this happens.

Supratim Pal

Numerade Educator

Problem 48

A wire loop is placed in a magnetic field that is perpendicular to the loop's plane. The field varies with time as shown in Figure 23.22. Rank the six periods of time in order of increasing magnitude of the induced emf. Indicate ties where appropriate.

Supratim Pal

Numerade Educator

Problem 49

A metal ring is dropped into a localized region of constant magnetic field, as indicated in Figure 23.23. The magnetic field is zero above and below the region. (a) At each of the three indicated locations ( 1,2 , and 3 ), is the induced current clockwise, counterclockwise, or zero? (b) Choose the best explanation from among the following:
A. The induced current is clockwise at 1 to oppose the field, zero at 2 because the field is uniform, and counterclockwise at 3 to maintain the field.

B. The induced current is counterclockwise at 1 to oppose the field, zero at 2 because the field is uniform, and clockwise at 3 to maintain the field.

C. The induced current is clockwise at 1 to oppose the field, clockwise at 2 to maintain the field, and clockwise at 3 to oppose the field.

Mark J

Numerade Educator

Problem 50

A $0.055-\mathrm{T}$ magnetic field passes through a circular ring of radius $3.1 \mathrm{~cm}$ at an angle of $16^{\circ}$ to the normal. Find the magnitude of the magnetic flux through the ring.

Vishal Gupta

Numerade Educator

Problem 51

A uniform magnetic field of magnitude $0.0250 \mathrm{~T}$ points vertically upward. Find the magnitude of the magnetic flux through each of the five sides of the open-topped rectangular box shown in Figure 23.24, given that the dimensions of the box are $L=32.5 \mathrm{~cm}, W=12.0 \mathrm{~cm}$, and $H=10.0 \mathrm{~cm}$.

TO

Tomi Obadiya

Numerade Educator

Problem 52

A magnetic field is oriented at an angle of $47^{\circ}$ to the normal of a rectangular area $5.1 \mathrm{~cm}$ by $6.8 \mathrm{~cm}$. If the magnetic flux through this area has a magnitude of $4.8 \times 10^{-5} \mathrm{~T} \cdot \mathrm{m}^{2}$, what is the strength of the magnetic field?

Vishal Gupta

Numerade Educator

Problem 53

Find the magnitude of the magnetic flux through the floor of a house that measures $22 \mathrm{~m}$ by $18 \mathrm{~m}$. Assume that the Earth's magnetic field at the location of the house has a north-pointing horizontal component of $2.6 \times 10^{-5} \mathrm{~T}$ and a downward vertical component of $4.2 \times 10^{-5} \mathrm{~T}$.

TO

Tomi Obadiya

Numerade Educator

Problem 54

The magnetic field produced by an MRI solenoid $2.5 \mathrm{~m}$ long and $1.2 \mathrm{~m}$ in diameter is $1.7 \mathrm{~T}$. Find the magnitude of the magnetic flux inside the core of this solenoid.

Vishal Gupta

Numerade Educator

Problem 55

A $0.45-\mathrm{T}$ magnetic field is perpendicular to a circular coil of wire with 53 loops and a radius of $15 \mathrm{~cm}$. If the magnetic field is reduced to zero in $0.12 \mathrm{~s}$, what is the magnitude of the induced emf in the coil?
56. Figure $23.25$ shows the magnetic flux through a wire loop as a function of time. What is the induced emf in the loop at (a) $t=0.050 \mathrm{~s}$, (b) $t=0.15 \mathrm{~s}$, and (c) $t=0.50 \mathrm{~s}$ ?

Vishal Gupta

Numerade Educator

Problem 56

Figure $23.25$ shows the magnetic flux through a wire loop as a function of time. What is the induced emf in the loop at (a) $t=0.050 \mathrm{~s}$, (b) $t=0.15 \mathrm{~s}$, and (c) $t=0.50 \mathrm{~s}$ ?

Supratim Pal

Numerade Educator

Problem 57

The magnetic flux through a wire loop is plotted in Figure $23.25$. (a) Is the magnitude of the induced emf at $t=0.25 \mathrm{~s}$ greater than, less than, or the same as the magnitude of the induced emf at $t=0.55 \mathrm{~s}$ ? Explain. (b) Calculate the magnitude of the induced emf at $t=0.25 \mathrm{~s}$ and $t=0.55 \mathrm{~s}$.

Supratim Pal

Numerade Educator

Problem 58

A conducting loop has an area of $7.4 \times 10^{-2} \mathrm{~m}^{2}$ and a resistance of $110 \Omega$. Perpendicular to the plane of the loop is a magnetic field of strength $0.48 \mathrm{~T}$. At what rate (in $\mathrm{T} / \mathrm{s}$ ) must this field change if the induced current in the loop is to be $0.32 \mathrm{~A}$ ?

Vishal Gupta

Numerade Educator

Problem 59

A metal rod $0.76 \mathrm{~m}$ long moves with a speed of $2.0 \mathrm{~m} / \mathrm{s}$ perpendicular to a magnetic field. If the induced emf between the ends of the rod is $0.45 \mathrm{~V}$, what is the strength of the magnetic field?

Vishal Gupta

Numerade Educator

Problem 60

A Boeing KC-135A airplane has a wingspan of $39.9 \mathrm{~m}$ and flies at a constant altitude near the North Pole with a speed of $850 \mathrm{~km} / \mathrm{h}$. If Earth's magnetic field is $5.0 \times 10^{-6} \mathrm{~T}$ at that location, what is the induced emf between the wing tips of the airplane?

Vishal Gupta

Numerade Educator

Problem 61

A metal rod with resistance $R$ can slide without friction on two zero-resistance rails, as shown in Figure 23.26. The rod and the rails are within a region of constant magnetic field pointing out of the page. Describe the motion of the rod when the switch is closed and be sure to include the effects of motional emf.

Supratim Pal

Numerade Educator

Problem 62

A conducting rod slides on two wires in a region with a magnetic field. The two wires are not connected. Is a force required to keep the rod moving with constant speed? Explain.

Sanjeev Kumar

Numerade Educator

Problem 63

The maximum emf of a certain generator is $100 \mathrm{~V}$. Suppose the magnetic field in the generator is doubled and the angular speed is tripled. What is the new maximum emf?

Vishal Gupta

Numerade Educator

Problem 64

The maximum emf of a certain generator is $100 \mathrm{~V}$. Suppose the magnetic field in the generator is halved and the area of the loops is tripled. What is the new maximum emf?

Vishal Gupta

Numerade Educator

Problem 65

The maximum induced emf in a generator rotating at $22 \mathrm{rad} / \mathrm{s}$ is $45 \mathrm{~V}$. How fast must the rotor of the generator rotate if it is to generate a maximum induced emf of $55 \mathrm{~V}$ ?

Vishal Gupta

Numerade Educator

Problem 66

A rectangular coil $25 \mathrm{~cm}$ by $35 \mathrm{~cm}$ has 120 loops. This coil produces a maximum emf of $65 \mathrm{~V}$ when it rotates with an angular speed of $190 \mathrm{rad} / \mathrm{s}$ in a magnetic field of strength $B$. Find the value of $B$.

Prabhat Tyagi

Numerade Educator

Problem 67

A 1.6-m wire is wound into a coil with a radius of $3.2 \mathrm{~cm}$. If this coil is rotated at $85 \mathrm{rpm}$ in a $0.075-\mathrm{T}$ magnetic field, what is its maximum emf?

Sanjeev Kumar

Numerade Educator

Problem 68

A circular coil with a diameter of $22.0 \mathrm{~cm}$ and 155 loops rotates about a vertical axis with an angular speed of $1250 \mathrm{rpm}$. The only magnetic field experienced by the system is that of the Earth. At the location of the coil, the horizontal component of this magnetic field is $3.80 \times 10^{-5} \mathrm{~T}$, and the vertical component is $2.85 \times 10^{-5} \mathrm{~T}$. (a) Which component of the magnetic field is important when calculating the induced emf in this coil? Explain. (b) Find the maximum emf induced in the coil.

Vishal Gupta

Numerade Educator

Problem 69

How can the rms voltage of an $\mathrm{AC}$ circuit be nonzero when its average value is zero? Explain.

Vishal Gupta

Numerade Educator

Problem 70

What changes must be made to the DC power formula, $P=I V$, for it to give the average power in an $\mathrm{AC}$ circuit?

Vishal Gupta

Numerade Educator

Problem 71

Consider four transformers (A, B, C, and D) for which the voltage in the primary coil is $V_{\mathrm{p}}$, the number of loops in the primary coil is $N_{\mathrm{p}}$, and the number of loops in the secondary coil is $N_{\mathrm{s}}$. Rank the transformers in order of increasing voltage in the secondary coil. Indicate ties where appropriate.
$$
\begin{array}{|c|c|c|c|}
\hline \text { Transformer } & \boldsymbol{V}_{p}(\mathbf{V}) & \boldsymbol{N}_{p} & \boldsymbol{N}_{s} \\
\hline \text { A } & 100 & 20 & 100 \\
\hline \text { B } & 100 & 100 & 20 \\
\hline \text { C } & 20 & 50 & 50 \\
\hline \text { D } & 50 & 400 & 800 \\
\hline
\end{array}
$$

Vishal Gupta

Numerade Educator

Problem 72

Suppose the number of loops in the secondary coil of a transformer is decreased. (a) Does the voltage in the secondary circuit increase, decrease, or stay the same? Explain. (b) Does the current in the secondary circuit increase, decrease, or stay the same? Explain.

Vishal Gupta

Numerade Educator

Problem 73

Transformer 1 has a primary voltage $V_{\mathrm{p}}$ and a secondary voltage $V_{\mathrm{s}}$. Transformer 2 has twice the number of loops in both its primary and secondary coils as transformer 1 does. If the primary voltage of transformer 2 is $2 V_{\mathrm{p}}$, what is its secondary voltage? Explain.

Vishal Gupta

Numerade Educator

Problem 74

Transformer 1 has a primary current $I_{\mathrm{p}}$ and a secondary current $I_{\mathrm{s}}$. Transformer 2 has twice as many loops on its primary coil as transformer 1 does, and both transformers have the same number of loops on the secondary coil. If the primary current of transformer 2 is $3 I_{\mathrm{p}}$, what is its secondary current? Explain.

Vishal Gupta

Numerade Educator

Problem 75

An AC generator produces a peak voltage of $55 \mathrm{~V}$. What is the rms voltage of this generator?

Vishal Gupta

Numerade Educator

Problem 76

European Electricity In many European homes the rms voltage from wall sockets is $240 \mathrm{~V}$. What is the maximum voltage in this case?

Vishal Gupta

Numerade Educator

Problem 77

An rms voltage of $120 \mathrm{~V}$ produces a maximum current of $2.1 \mathrm{~A}$ in a certain resistor. Find the resistance of this resistor.

Vishal Gupta

Numerade Educator

Problem 78

The rms current in an $\mathrm{AC}$ circuit with a resistance of $150 \Omega$ is $0.85$ A. What are (a) the average power and (b) the maximum power consumed by this circuit?

Vishal Gupta

Numerade Educator

Problem 79

A 3.33-k $\Omega$ resistor is connected to an $\mathrm{AC}$ generator with a maximum voltage of $141 \mathrm{~V}$. Find (a) the average power and (b) the maximum power delivered to this circuit.

Vishal Gupta

Numerade Educator

Problem 80

The electric motor in a toy train requires a voltage of $3.0 \mathrm{~V}$. Find the ratio of loops on the primary coil to loops on the secondary coil in a transformer that will step down the 110 -V household voltage to $3.0 \mathrm{~V}$.

Vishal Gupta

Numerade Educator

Problem 81

A disk drive plugged into a $120-\mathrm{V}$ outlet operates on a voltage of $9.0 \mathrm{~V}$. The transformer that powers the disk drive has 147 loops on its primary coil. (a) Should the number of loops on the secondary coil be greater than or less than 147? Explain. (b) Find the number of loops on the secondary coil.

Vishal Gupta

Numerade Educator

Problem 82

A transformer with a loops ratio (secondary/primary) of $1 / 18$ is used to step down the voltage from a 110 -V wall socket to power a battery recharging unit. What is the voltage supplied to the recharger?

Vishal Gupta

Numerade Educator

Problem 83

A neon sign that requires a voltage of $11,000 \mathrm{~V}$ is plugged into a $120-\mathrm{V}$ wall outlet. What loops ratio (secondary/ primary) must a transformer have to power the sign?

Vishal Gupta

Numerade Educator

Problem 84

A lightbulb uses an average power of $75 \mathrm{~W}$ when connected to a source that supplies an rms voltage of $120 \mathrm{~V}$. (a) What is the resistance of the lightbulb?
(b) What is the maximum current in the bulb? (c) What is the maximum power used by the bulb at any given instant of time?

Vishal Gupta

Numerade Educator

Problem 85

You hold a circular loop of wire at the north magnetic pole of the Earth. Consider the magnetic flux through this loop due to Earth's magnetic field. Is the flux when the normal to the loop is horizontal greater than, less than, or equal to the flux when the normal is vertical? Explain.

Vishal Gupta

Numerade Educator

Problem 86

A bar magnet with its north pole facing downward is falling toward the center of a horizontal conducting ring. As viewed from above, is the direction of the induced current in the ring clockwise or counterclockwise?
Explain.

Vishal Gupta

Numerade Educator

Problem 87

Figure $23.27$ shows a zero-resistance rod sliding toward the right on two zero-resistance rails that are separated by the distance $L=0.450 \mathrm{~m}$. The rails are connected by a $12.5-\Omega$ resistor, and the entire system is in a uniform magnetic field with a magnitude of $0.750 \mathrm{~T}$. Find the speed at which the bar must move to produce a current of $0.125 \mathrm{~A}$ in the resistor.

Vishal Gupta

Numerade Educator

Problem 88

Figure $23.28$ shows a current-carrying wire and a circuit containing a resistor $R$. (a) If the current in the wire is constant, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain. (b) If the current in the wire increases in magnitude, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain.

Vishal Gupta

Numerade Educator

Problem 89

A loop of wire is dropped and allowed to fall between the poles of a horseshoe magnet, as shown in Figure 23.29. State whether the induced current in the loop is clockwise or counterclockwise when (a) the loop is above the magnet and (b) the loop is below the magnet.

Vishal Gupta

Numerade Educator

Problem 90

The Voyager I spacecraft moves through interstellar space with a speed of $8.0 \times 10^{3} \mathrm{~m} / \mathrm{s}$. The magnetic field in this region of space has a magnitude of $2.0 \times 10^{-10} \mathrm{~T}$. Assuming that the $5.0-\mathrm{m}$-long antenna on the spacecraft is at right angles to the magnetic field, find the motional emf between its ends.

Supratim Pal

Numerade Educator

Problem 91

Consider a $5.8 \mathrm{~cm}$ by $8.2 \mathrm{~cm}$ rectangular loop of wire in a uniform magnetic field of magnitude $1.3 \mathrm{~T}$. The loop is rotated from a position where the magnetic flux is zero to a position of maximum flux in $21 \mathrm{~ms}$. What is the average induced emf in the loop?

Vishal Gupta

Numerade Educator

Problem 92

Predict \& Explain Figure $23.30$ shows two metal disks of the same size and material oscillating in and out of a region with a magnetic field. One disk is solid; the other has a series of slots. (a) Is the effect of eddy currents on the solid disk greater than, less than, or equal to their effect on the slotted disk? (b) Choose the best explanation from among the following:

A. The solid disk experiences a greater force because eddy currents in it flow freely and are not interrupted by the slots.

B. The slotted disk experiences the greater force because the slots allow more magnetic field to penetrate the disk. C. The disks are the same size and made of the same material; therefore, they experience the same force.

Vishal Gupta

Numerade Educator

Problem 93

Transcranial magnetic stimulation (TMS) is a noninvasive method for studying brain function. In TMS a conducting loop is held near a person's head, as shown in Figure $23.31$. When the current in the loop is changed rapidly, the magnetic field it creates can change at the rate of $3.00 \times 10^{4} \mathrm{~T} / \mathrm{s}$. This rapidly changing magnetic field induces an electric current in a restricted region of the brain that can cause a finger to twitch, bright spots to appear in the visual field (called magnetophosphenes), or an overwhelming feeling of complete happiness. If the magnetic field changes at the previously mentioned rate over an area of $1.13 \times 10^{-2} \mathrm{~m}^{2}$, what is the induced emf?

Vishal Gupta

Numerade Educator

Problem 94

Write a report on electric guitars. When was the first one made, and who invented it? When were electric guitars first used in professional performances? How many pickups do various electric guitars have? How are the different pickups used? How does a whammy bar work?

Nick Johnson

Numerade Educator

Problem 95

Present several examples of everyday devices that apply Faraday's law of induction. How is the change in magnetic flux produced? How is the induced emf or the induced current used?

Shannon Wesley

Numerade Educator

Problem 96

Suppose the downward-pointing vertical component of the magnetic field increases as a car drives over a loop detector. As viewed from above, is the induced current in the loop clockwise, counterclockwise, or zero?

Vishal Gupta

Numerade Educator

Problem 97

A car drives onto a loop detector and increases the downward-pointing component of the magnetic field within the loop from $1.2 \times 10^{-5} \mathrm{~T}$ to $2.6 \times 10^{-5} \mathrm{~T}$ in $0.38 \mathrm{~s}$. What is the induced emf in the detector if it is circular, has a radius of $0.67 \mathrm{~m}$, and consists of four loops of wire?
A. $0.66 \times 10^{-4} \mathrm{~V}$
C. $2.1 \times 10^{-4} \mathrm{~V}$
B. $1.5 \times 10^{-4} \mathrm{~V}$
D. $6.2 \times 10^{-4} \mathrm{~V}$

Supratim Pal

Numerade Educator

Problem 98

A truck drives onto a loop detector and increases the downward-pointing component of the magnetic field within the loop from $1.2 \times 10^{-5}$ T to a larger value, $B$, in $0.38 \mathrm{~s}$. The detector is circular, has a radius of $0.67 \mathrm{~m}$, and consists of three loops of wire. What is $B$, given that the induced emf is $8.1 \times 10^{-4} \mathrm{~V} ?$
A. $3.6 \times 10^{-5} \mathrm{~T}$ B. $7.3 \times 10^{-5} \mathrm{~T}$
C. $8.5 \times 10^{-5} \mathrm{~T}$
D. $24 \times 10^{-5} \mathrm{~T}$

Supratim Pal

Numerade Educator

Problem 99

A motorcycle can increase the downward-pointing component of the magnetic field within a loop only from $1.2 \times 10^{-5}$ T to $1.9 \times 10^{-5}$ T. Suppose the detector is square, $0.75 \mathrm{~m}$ on a side, and has four loops of wire. Over what period of time must the magnetic field increase if it is to induce an emf of $1.4 \times 10^{-4} \mathrm{~V} ?$
A. $0.028 \mathrm{~s}$
C. $0.35 \mathrm{~s}$
B. $0.11 \mathrm{~s}$
D. $0.60 \mathrm{~s}$

Supratim Pal

Numerade Educator