College Physics Explore and Apply

Eugenia Etkina; Alan Van Heuvelen; Gorazd Planinši?

Chapter 21

Electromagnetic Induction - all with Video Answers

Educators

Chapter Questions

Problem 1

You and your friend are performing experiments in a physics lab. Your friend claims that in general, something has to move in order to induce a current in a coil that has no battery. What experiments can you perform to support her idea? What experiments can you perform to reject it?

Vishal Gupta

Vishal Gupta

Numerade Educator

Problem 2

You decide to use a metal ring as an indicator of induced current. If there is a current, the ring will feel warm in your hand. You place the ring around a solenoid as shown in Figure $P 21.2,$ position I. Will the ring feel warm if the solenoid is connected to (a) a DC power supply or
(b) an AC power supply? (c) Answer questions
(a) and (b) for the case when the ring is parallel to the solenoid (position II). Explain your
answers.

Vishal Gupta

Numerade Educator

Problem 3

To check whether a lightbulb permanently attached to a coil is still good, you place the coil next to another coil that is attached to a battery, as shown in Figure P21.3. Explain how or whether each of the following actions can help you determine if the lightbulb works.
(a) Close the switch in circuit A.
(b) Keep the switch in circuit A closed.
(c) Open the switch in circuit A. Indicate any assumptions that you made.

Vishal Gupta

Numerade Educator

Problem 4

$\mathrm{A}$ flashlight that operates without batteries is lying on your desk. The light illuminates only when you repeatedly squeeze the flashlight's handle. You notice that paper clips tend to stick to the outside of the flashlight. What physical mechanism might control the operation of the flashlight?

Vishal Gupta

Numerade Educator

Problem 5

You need to invent a practical application for a coil of wire that detects the vibrations or movements of a nearby magnet. Describe your invention. (The application should not repeat any described in this book.)

Vishal Gupta

Numerade Educator

Problem 6

Describe how you will design a device that uses electromagnetic induction to detect a burglar opening a window in your ground floor apartment. Include drawings and a word description.

Vishal Gupta

Numerade Educator

Problem 7

A coil connected to an ammeter can detect alternating currents in other circuits. Explain how this system might work. Could you use it to eavesdrop on a telephone conversation being transmitted through a wire?

Averell Hause

Carnegie Mellon University

Problem 8

The $\vec{B}$ field in a region has a magnitude of $0.40 \mathrm{T}$ and points in the positive $z$ -direction, as shown in Figure $P 21.8$. Determine the magnetic flux through
(a) surface abcd,
(b) surface bcef, and
(c) surface adef.

Vishal Gupta

Numerade Educator

Problem 9

How do you position a bicycle tire so that the magnetic flux through it due to Earth's magnetic field is as large as possible? Estimate this maximum flux. What assumptions did you make?

Vishal Gupta

Numerade Educator

Problem 10

Estimate the magnetic flux through your head when the $\vec{B}$ field of a 1.4-T MRI machine passes through your head.

Vishal Gupta

Numerade Educator

Problem 11

Estimate the magnetic flux through the south- and west-facing windows of a house in British Columbia, where Earth's $\vec{B}$ field has a magnitude of $5.8 \times 10^{-5} \mathrm{T}$ and points roughly north with a downward inclination of $72^{\circ} .$ Explain how you made the estimates.

Vishal Gupta

Numerade Educator

Problem 12

You perform experiments using an apparatus that has two insulated wires wrapped around a cardboard tube (Figure $\mathrm{P} 21.3$ ). Determine the direction of the current in the bulb when (a) the switch is closing and the current in coil A is increasing, (b) the switch has just closed and there is a steady current in coil $\mathrm{A},$ and $(\mathrm{c})$ the switch has just opened and the current in coil A is decreasing.

Vishal Gupta

Numerade Educator

Problem 13

You have the apparatus shown in Figure P21.13. A circular metal plate swings past the north pole of a permanent magnet. The metal consists of a series of rings of increasing radius. Indicate the direction of the current in
one ring (a) as the metal swings down from the left into the magnetic field and (b) as the metal swings up toward the right out of the magnetic field. Use Lenz's law to justify your answers.

Vishal Gupta

Numerade Educator

Problem 14

You suggest that eddy currents can stop the motion of a steel disk that vibrates while hanging from a spring. Explain how you can do this without touching the disk.

Vishal Gupta

Numerade Educator

Problem 15

Your friend thinks that an induced magnetic field is always opposite the changing external field that induces an electric current. Provide a counterexample to your friend's claim. Discuss why your friend's idea would violate conservation of energy.

Vishal Gupta

Numerade Educator

Problem 16

The magnetic flux through three different coils is changing as shown in Figure P21.16. For each situation, draw a corresponding graph showing qualitatively how the induced emf changes with time.

Vishal Gupta

Numerade Educator

Problem 17

The magnetic flux through three different coils is changing as shown in Figure P21.17. For each situation, draw a corresponding graph showing quantitatively how the induced emf changes with time.

Vishal Gupta

Numerade Educator

Problem 18

A magnetic field passing through two coils of the same diameter and length decreases from a magnitude of $B_{\text {ex }}$ to zero in the time interval $\Delta t .$ The first coil has twice the number of turns as the second. (a) Compare the emfs induced in the coils. (b) How can you change the experiment so that the emfs produced in them are the same?

Vishal Gupta

Numerade Educator

Problem 19

In transcranial magnetic stimulation (TMS) an abrupt decrease in the electric current in a small coil placed on the scalp produces an abrupt decrease in the magnetic field inside the brain. Suppose the magnitude of the $\vec{B}$ field changes from $0.80 \mathrm{T}$ to $0 \mathrm{T}$ in $0.080 \mathrm{s}$. Determine the induced emf around a small circle of brain tissue of radius $1.2 \times 10^{-3} \mathrm{m} .$ The $\vec{B}$ field is perpendicular to the surface area of the circle of brain tissue.

Vishal Gupta

Numerade Educator

Problem 20

To measure a magnetic field produced by an electromagnet, you use a circular coil of radius $0.30 \mathrm{m}$ with 25 loops (resistance of $25 \Omega$ ) that rests between the poles of the magnet and is connected to an ammeter. While the current in the electromagnet is reduced to zero in $1.5 \mathrm{s}$, the ammeter in the coil shows a steady reading of 180 mA. Draw a picture of the experimental setup and determine everything you can about the electromagnet.

Vishal Gupta

Numerade Educator

Problem 21

You want to use the idea of electromagnetic induction to make the bulb from your small flashlight glow; it glows when the potential difference across it is 1.5 V. You have a small bar magnet and a coil with 100 turns, each with area $3.0 \times 10^{-4} \mathrm{m}^{2} .$ The magnitude of the $\vec{B}$ field at the front of the bar magnet's north pole is $0.040 \mathrm{T}$ and reaches $0 \mathrm{T}$ when it is about $4 \mathrm{cm}$ away from the pole. Can you make the bulb light? Explain.

Vishal Gupta

Numerade Educator

Problem 22

An apnea monitor for adults consists of a flexible coil that wraps around the chest (Figure P21.22). When the patient inhales, the chest expands, as does the coil. Earth's $\vec{B}$ field of $5.0 \times 10^{-5} \mathrm{T}$ passes through the coil at a $53^{\circ}$ angle relative to a line perpendicular to the coil. Determine the average induced emf in such a coil during one inhalation if the 300 -turn coil area increases by $42 \mathrm{cm}^{2}$ during $2.0 \mathrm{s}$.

Vishal Gupta

Numerade Educator

Problem 23

A bar magnet induces a current in an $N$ -turn coil as the magnet moves closer to it (Figure $P 21.23$ ). The coil's radius is $R \mathrm{cm},$ and the average induced emf across the bulb during the time interval is $\mathcal{E}$ V. (a) Make a list of the physical quantities that you can determine using this information; (b) Is the direction of the induced current from lead a to b, or from b to a? Explain.

Vishal Gupta

Numerade Educator

Problem 24

You have a coil of wire with 10 turns each of $1.5-\mathrm{cm}$ radius. You place the plane of the coil perpendicular to a $0.40-\mathrm{T} \vec{B}$ field produced by the poles of an electromagnet (Figure Q21.2). (a) Find the magnitude of the average induced emf in the coil when the magnet is turned off and the field decreases to $0 \mathrm{T}$ in $2.4 \mathrm{s}$. (b) Is the direction of the induced current in the coil from lead a to b, or from b to a? Explain.

Vishal Gupta

Numerade Educator

Problem 25

An experimental apparatus has two parallel horizontal metal rails separated by $1.0 \mathrm{m}$. A $2.0-\Omega$ resistor is connected from the left end of one rail to the left end of the other. A metal axle with metal wheels is pulled toward the right along the rails at a speed of $20 \mathrm{m} / \mathrm{s}$. Earth's uniform $5.0 \times 10^{-5}-\mathrm{T}$ $\vec{B}$ field points down at an angle of $53^{\circ}$ below the horizontal. Make a list of the physical quantities you can determine using this information and determine two of them.

Vishal Gupta

Numerade Educator

Problem 26

A Boeing 747 with a $65-\mathrm{m}$ wingspan is cruising northward at $250 \mathrm{m} / \mathrm{s}$ toward Alaska. The $\vec{B}$ field at this location is $5.0 \times 10^{-5} \mathrm{T}$ and points $60^{\circ}$ below its direction of travel. Determine the potential difference between the tips of its wings.

Vishal Gupta

Numerade Educator

Problem 27

A circular loop of radius $9.0 \mathrm{cm}$ is placed perpendicular to a uniform $0.35-\mathrm{T} \vec{B}$ field. You collapse the loop into a long, thin shape in $0.10 \mathrm{s}$ What is the average induced emf while the loop is being reshaped? What assumptions did you make?

Vishal Gupta

Numerade Educator

Problem 28

Suppose a power line produces a $6.0 \times 10^{-4}-\mathrm{T}$ peak magnetic field 60 times each second at the location of a neuron brain cell of radius $6.0 \times 10^{-6} \mathrm{m} .$ Estimate the maximum magnitude of the induced emf around the perimeter of this cell during one-half cycle of magnetic field change.

Vishal Gupta

Numerade Educator

Problem 29

You need to test Faraday's law. You have a 12 -turn rectangular coil that measures $0.20 \mathrm{m} \times 0.40 \mathrm{m}$ and an electromagnet that produces a $0.25-\mathrm{T}$ magnetic field in a well-defined region that is larger than the area of the coil. You also have a stopwatch, an ammeter, a voltmeter, and a motion detector.
(a) Describe an experiment you will design to test Faraday's law.
(b) How will you calculate the measurable outcome of this experiment using the materials available? (c) Describe how you can test Lenz's law with this equipment.

Mayukh Banik

Numerade Educator

Problem 30

You build a coil of radius $r(\mathrm{m})$ and place it in a uniform $\vec{B}$ field oriented perpendicular to the coil's surface. What is the total electric charge that passes through the coil's wire loops if the $\vec{B}$ field decreases at a constant rate to zero? The resistance of the coil's wire is $R(\Omega)$.

Vishal Gupta

Numerade Educator

Problem 31

Invent a problem for which the following equation might be a solution.
$$0.01 \mathrm{V}=(100) \frac{(A) \cos 0^{\circ}(0.12 \mathrm{T}-0)}{(1.2 \mathrm{s}-0)}$$

Vishal Gupta

Numerade Educator

Problem 32

Invent a problem for which the following equation might be a solution.
$$0.01 \mathrm{V}=100 \frac{\pi(0.10 \mathrm{m})^{2}(0.12 \mathrm{T})\left(\cos 0^{\circ}-\cos 90^{\circ}\right)}{(t-0)}$$

Vishal Gupta

Numerade Educator

Problem 33

Equation Jeopardy 3 Invent a problem for which the following equation might be a solution.
$$\mathcal{E}=-(35) \frac{(0.12 \mathrm{T})\left(\cos 0^{\circ}\right)\left[(0)^{2}-\pi(0.10 \mathrm{m})^{2}\right]}{(3.0 \mathrm{s}-0)}$$

Vishal Gupta

Numerade Educator

Problem 34

Astronauts on a space station decide to use Earth's magnetic field to generate electric current. Earth's $\vec{B}$ field in this region has the magnitude of $3.0 \times 10^{-7}$ T. They have a coil that rotates $90^{\circ}$ in 1.2 s. The area inside the coil measures $5000 \mathrm{m}^{2}$. Estimate the number of loops needed in the coil so that during that $90^{\circ}$ turn it produces an average induced emf of about $120 \mathrm{V}$. Indicate any assumptions you made. Is this a feasible way to produce electric energy?

Vishal Gupta

Numerade Educator

Problem 35

A toy electric generator has a 20-turn circular coil with each turn of radius $1.8 \mathrm{cm} .$ The coil resides in a $1.0-\mathrm{T}$ magnitude $\vec{B}$ field. It also has a lightbulb that lights if the potential difference across it is about 1 V. You start rotating the coil, which is initially perpendicular to the $\vec{B}$ field. (a) Determine the time interval needed for a $90^{\circ}$ rotation that will produce an average induced emf of $1.0 \mathrm{V}$. (b) Use a proportion technique to show that the same emf can be produced if the time interval for one rotation is reduced to one-fourth while the radius of the coil is reduced by one-half.

Vishal Gupta

Numerade Educator

Problem 36

A generator has a 450-turn coil that is $10 \mathrm{cm}$ long and $12 \mathrm{cm}$ wide. The coil rotates at 8.0 rotations per second in a $0.10-\mathrm{T}$ magnitude $\vec{B}$ field. Determine the generator's peak voltage.

Vishal Gupta

Numerade Educator

Problem 37

You need to make a generator for your bicycle light that will provide an alternating emf whose peak value is $4.2 \mathrm{V}$. The generator coil has 55 turns and rotates in a 0.040-T magnitude $\vec{B}$ field. If the coil rotates at 400 revolutions per second, what must the area of the coil be to develop this emf? Describe any problems with this design (if there are any).

Vishal Gupta

Numerade Educator

Problem 38

A British bicycle light company advertises flashing bicycle lights that require no batteries and produce no resistance to riding. A magnet attached to a spoke on the bicycle tire moves past a generator coil on the bicycle frame, inducing an emf that causes a light to flash. The magnet and coil never touch. Does this lighting system really produce no resistance to riding? Justify your answer.

Vishal Gupta

Numerade Educator

Problem 39

A generator has a 100 -turn coil that rotates in a $0.30-\mathrm{T}$ magnitude $\vec{B}$ field at a frequency of 80 Hz $(80$ rotations per second) causing a peak emf of 38 V. (a) Determine the area of each loop of the coil.
(b) Write an expression for the emf as a function of time (assuming the emf is zero at time zero).
(c) Determine the emf at 0.0140 s.

Vishal Gupta

Numerade Educator

Problem 40

A $10-\mathrm{Hz}$ generator produces a peak emf of $40 \mathrm{V} .$ (a) Write an expression for the emf as a function of time. Indicate your assumptions. (b) Determine the emf at the following times: $0.025 \mathrm{s}, 0.050 \mathrm{s}, 0.075 \mathrm{s},$ and $0.100 \mathrm{s}$.
(c) Plot these emf-versus-time data on a graph and connect the points with a smooth curve.

Vishal Gupta

Numerade Educator

Problem 41

A rectangular wire loop is moving with constant speed through a region of uniform $\vec{B}$ field that points into the page (Figure $P 21.41$ ). The longer side of the loop is twice the width of the magnetic field region. Draw a qualitative graph that shows how the induced current in the loop depends on time during the period in which the loop moves from the position shown in the figure to the position where the left side of the loop exits the magnetic field. Assume that a counterclockwise direction of the current is positive.

Vishal Gupta

Numerade Educator

Problem 42

A wire loop consists of two equal parts that are connected so that they form a "rectangular figure eight." The loop is moving with constant speed through a region of uniform $\vec{B}$ field that points into the page (Figure $P 21.42$ ). The longer side of the loop is twice the width of the magnetic field region. Draw a qualitative graph that shows how the induced current in the loop depends on time during the period in which the loop moves from the position shown in the figure to the position where the left side of the loop exits the magnetic field. Assume that a counterclockwise direction of the current in the right half of the loop is positive.

Vishal Gupta

Numerade Educator

Problem 43

The voltage across an AC power supply is given by $\Delta V_{\mathrm{AC}}=(100 \mathrm{V}) \sin (2 \pi 50 t) .$ Determine (a) $\Delta V_{\mathrm{rms}},(\mathrm{b})$ the period with
which the voltage vibrates, (c) the amplitude of the current through the $200-\Omega$ resistor that is connected to this power supply, and (d) the average power transferred by the power supply to the resistor.

Vishal Gupta

Numerade Educator

Problem 44

The alternating current through a $2.0-\mu \mathrm{F}$ capacitor is given by $I_{\mathrm{C}}=(0.04 \mathrm{A}) \sin (2 \pi 400 t) .$ Determine (a) the rms voltage across the capacitor and (b) the shortest time interval between the peak of the voltage across the capacitor and the peak of the current through the capacitor.
(c) How will the answers to questions (a) and (b) change if the capacitance is doubled? Explain.

Vishal Gupta

Numerade Educator

Problem 45

The alternating current through a solenoid is given by $I_{\mathrm{L}}=(3.2 \mathrm{A}) \sin (2 \pi 180 t),$ and the $\mathrm{rms}$ voltage across the solenoid is 190 V. Determine (a) the inductance of the solenoid and (b) the shortest time interval between the peak of the voltage across the solenoid and the peak of the current through the solenoid, assuming that the resistance of the solenoid can be ignored. (c) A nickel cylinder with a relative magnetic permeability of 300 is inserted into the solenoid. Determine the new amplitude of the current through the solenoid, assuming that the solenoid remains connected to the same power supply.

Vishal Gupta

Numerade Educator

Problem 46

The rms voltage of household AC in Europe is 230 V. Determine (a) the amplitude of the alternating voltage across and (b) the amplitude of the alternating current through a $100-$ W European incandescent lightbulb. Determine (c) the resistance of this lightbulb and (d) the power output of the lightbulb when you use it in the United States, where the rms voltage is $120 \mathrm{V} .$ Indicate any assumptions that you made.

Vishal Gupta

Numerade Educator

Problem 47

You build a parallel plate capacitor by placing a 0.1-mm-thick sheet of paper between two $100-\mathrm{cm}^{2}$ pieces of aluminum foil. The dielectric constant of paper is $2.3 .$ Determine (a) the capacitance of the capacitor and (b) the frequency of the alternating current at which the capacitive reactance of the capacitor is equal to $5 \Omega .$

Vishal Gupta

Numerade Educator

Problem 48

You have a $100-\mathrm{m}$ copper wire with cross-sectional area $0.20 \mathrm{mm}^{2}$ and resistivity $1.7 \times 10^{-8} \Omega \cdot \mathrm{m} .$ You make a 780 -turn solenoid by winding the wire on a plastic tube (diameter $4.0 \mathrm{cm},$ length $10.0 \mathrm{cm}$ ). Determine
(a) the resistance of the solenoid, (b) the inductance of the solenoid, and
(c) the frequency of the alternating current at which the inductive reactance of the solenoid is equal to its resistance.

Vishal Gupta

Numerade Educator

Problem 49

You need to build a transformer that can step the emf up from $120 \mathrm{V}$ to $12,000 \mathrm{V}$ to operate a neon sign for a restaurant. What will be the ratio of the secondary to primary turns of this transformer?

Vishal Gupta

Numerade Educator

Problem 50

Your home's electric doorbell operates on $10 \mathrm{V}$. Should you use a step-up or step-down transformer in order to convert the home's $120 \mathrm{V}$ to $10 \mathrm{V} ?$ Determine the ratio of the secondary to primary turns needed for the bell's transformer.

Vishal Gupta

Numerade Educator

Problem 51

A $9.0-\mathrm{V}$ battery and switch are connected in series across the primary coil of a transformer. The secondary coil is connected to a lightbulb that operates on $120 \mathrm{V}$. Draw the circuit. Describe in detail how you can get the bulb to light-not necessarily continuously.

Vishal Gupta

Numerade Educator

Problem 52

You are fixing a transformer for a toy truck that uses an $8.0-\mathrm{V}$ rms voltage to run it. The primary coil of the transformer is broken; the secondary coil has 30 turns. The primary coil is connected to a $120-\mathrm{V}$ wall outlet.
(a) How many turns should you have in the primary coil? (b) If you then connect this primary coil to a $240-\mathrm{V}$ rms voltage, what will be the amplitude of the alternating voltage across the secondary coil?

Vishal Gupta

Numerade Educator

Problem 53

A wire loop has a radius of $10 \mathrm{cm}$. A changing external magnetic field causes an average $0.60-\mathrm{N} / \mathrm{C}$ electric field in the wire. (a) Determine the work that the electric field does in pushing $1.0 \mathrm{C}$ of electric charge around the loop. (b) Determine the induced emf caused by the changing magnetic field. (c) You measure a 0.10 - A electric current. What is the electrical resistance of the loop?

Mayukh Banik

Numerade Educator

Problem 54

You are hired to advise the coach of the Olympic ice-skating team concerning an idea for a costume for one of the skaters. They want to put a flat coil of wire on the front of the skater's torso and connect the ends of the coil to lightbulbs on the skater's belt. They hope that the bulbs will light when the skater spins in Earth's magnetic field. Do you think that the system will work? If so, could you provide specifications for the device and justification for your advice?

Anna Zeng

Numerade Educator

Problem 55

A hammerhead shark (Figure $P 21.55)$ has a 0.90-m-wide head. The shark swims north at $1.8 \mathrm{m} / \mathrm{s} .$ Earth's $\vec{B}$ field at this location is $5.0 \times 10^{-5}$ T and points $30^{\circ}$ below the direction of the shark's travel. Determine the potential difference between the two sides of the shark's head.

Vishal Gupta

Numerade Educator

Problem 56

You are an inventor and want to develop a braking system that not only stops the car but also converts the original kinetic energy to some other useful energy. One of your ideas is to connect a rotor coil (the rotating coil of the generator) to the turning axle of the car. When you press on the brake pedal, a switch turns on a steady electric current to a stationary coil (an electromagnet called the stator) that produces a steady magnetic field in which the rotor turns. You now have a generator that produces an alternating current and an induced emf - electric power. Make a simple drawing of the rotor and stator at one instant and determine the direction of the magnetic force exerted on the rotor. Does this force help stop the car? Explain.

Raj Bala

Numerade Educator

Problem 57

Your professor asks you to help design an electromagnetic induction sparker (a device that produces sparks). Include drawings and word descriptions for how it might work, details of its construction, and a description of possible problems.

Mayukh Banik

Numerade Educator

Problem 58

In a new lab experiment, two parallel vertical metal rods are separated by $1.0 \mathrm{m} .$ A $2.0-\Omega$ resistor is connected from the top of one rod to the top of the other. A 0.20-kg horizontal metal bar falls between the rods and makes contact at its ends with the rods. A $\vec{B}$ field of $0.50 \times 10^{-4} \mathrm{T}$ points horizontally between the rods. The bar should eventually reach a terminal falling velocity (constant speed) when the magnetic force of the magnetic field on the induced current in the bar balances the downward force due to the gravitational pull of the Earth. (a) Develop in symbols an expression for the current through the bar as it falls. (b) Determine in symbols an expression for the magnetic force exerted on the falling bar (and determine the direction of that force). Remember that an electric current passes through it, and the bar is falling in the magnetic field. (c) Determine the final constant speed of the falling bar (d) Is this process realistic? Explain.

Vishal Gupta

Numerade Educator

Problem 59

You have a $12-\mathrm{V}$ battery, some wire, a switch, and a separate coil of wire. (a) Design a circuit that will produce an emf around the coil even though it is not connected to the battery.
(b) Show, using appropriate equations, why your system will work. (c) Describe one application for your circuit.

Anna Zeng

Numerade Educator

Problem 60

You want to build a generator for a multi-day canoe trip. You have a fairly large permanent magnet, some wire, and a lightbulb. Design a generator and provide detailed specifications for it. (Ideas for the design could include cranking a handle or placing a paddle wheel that turns a coil in a nearby stream.)

Prashant Bana

Numerade Educator

Problem 61

A sparker used to ignite lighter fluid in a barbeque grill is shown in Figure P21.61. You compress a knob at the end of the sparker. This compresses a spring, which when released moves a magnet at the end of the knob quickly into a 200-turn coil. The change in flux through the coil induces an emf that causes a spark across the $0.10-\mathrm{mm}$ gap at the end of the sparker. (a) Estimate the time interval needed for the change in flux in order to produce this spark. Indicate any assumptions you made. (b) Is this a realistic process? Explain.

Mayukh Banik

Numerade Educator

Problem 62

Your friend needs to design an experiment that will allow her to measure the magnitude of the $\vec{B}$ field near a large permanent magnet. She has a small coil (50 turns, diameter 1.0 cm), a small motor that can spin at 300 revolutions per second, and an $\mathrm{AC}$ voltmeter that can measure voltage with $0.001-\mathrm{V}$ precision. (a) Describe in detail the experimental setup (using this equipment) that will allow your friend to estimate the magnitude of the $\vec{B}$ field. (b) Estimate the smallest value of the $\vec{B}$ field magnitude that she will be able to measure. Indicate any assumptions that you made.

Anna Zeng

Numerade Educator

Problem 63

Lightning is a sudden electrical discharge that occurs during a storm. In a typical cloud-to-ground lightning flash, a discharge current changes at a rate of about $10^{11} \mathrm{A} / \mathrm{s} .$ Estimate the maximum induced emf around the metal box of a typical computer during a lightning flash, assuming the lightning strikes the ground $200 \mathrm{m}$ from the computer. Describe any assumptions that you made. (Hint: Model the lightning as a long straight wire carrying current that changes in time.)

Prashant Bana

Numerade Educator

Problem 64

Jose needs an MRI (magnetic resonance imaging) scan. During the exam, Jose lies in a region of a very strong $1.5-\mathrm{T}$ horizontal magnetic field pointing from Jose's waist toward his head. A medical assistant moves Jose from the scanner, reducing the magnetic field from $1.5 \mathrm{T}$ to $0.1 \mathrm{T}$ in $1.0 \mathrm{s}$. Consequently, the $\vec{B}$ field through Jose's $0.3-\mathrm{m}$ by $0.4-\mathrm{m}$ chest decreases. The conductive tissue inside his body around the outer part of his chest is a loop, with the chest as the area inside this loop. (a) Estimate the induced emf around this conducting loop as the $\vec{B}$ field decreases. (b) If the resistance of his body tissue around this loop is $5 \Omega,$ what is the induced current passing around his body? (c) What is the direction of the current?

Vishal Gupta

Numerade Educator

Problem 65

A magstripe reader used to read a credit card number or a card key for a hotel room has a tiny coil that detects a changing magnetic field as tiny bar magnets pass by the coil. Calculate the magnitude of the induced emf in a magstripe card reader coil. Assume that the magstripe magnetic field changes at a constant rate of $500 \mathrm{mT} / \mathrm{ms}$ as the region between two tiny magnets on the stripe passes the coil. The reader coil is $2.0 \mathrm{mm}$ in diameter and has 5000 turns.

Vishal Gupta

Numerade Educator

Problem 66

Show that when a metal rod $L$ meters long moves at speed $v$ perpendicular to $\vec{B}$ field lines, the magnetic force exerted by the field on the electrically charged particles in the rod produces a potential difference between the ends of the rod equal to the product $B L v$.

Vishal Gupta

Numerade Educator

Problem 67

Magnetic braking brings the car of the Tower of Terror ride to a stop from a speed of $161 \mathrm{km} / \mathrm{h}$. (a) Is its $161-\mathrm{km} / \mathrm{h}$ speed what you would expect of an object after a $115-\mathrm{m}$ fall? Explain. (b) Estimate the time interval for the free-fall part of its trip.
(c) Estimate the average acceleration of the car while stopping due to its magnetic braking.

Luis Rios

Numerade Educator

Problem 68

Why is the detected signal from an MIT apparatus greater if a moist conductive layer is near the surface?
(a) The signal is reflected better from the top of a nearby conductive layer.
(b) The induced current is greater if the soil is moist and conductive.
(c) The induced magnetic field from the induced current is bigger if its source is near the detection coil.
(d) All three of the above reasons
(e) $\mathrm{b}$ and $\mathrm{c}$

Mayukh Banik

Numerade Educator

Problem 69

All other conditions being equal, why is the induced current greater in claypan soil than in topsoil?
(a) Claypan soil has a higher concentration of magnetic ions compared to topsoil.
(b) Claypan soil is partly metallic in composition.
(c) Claypan soil has greater density than loose topsoil.
(d) The clay is closely packed, moist, and a better electrical conductor than loose, dry topsoil.

Anna Zeng

Numerade Educator

Problem 70

Why is MIT used to search for mineral deposits (iron, copper, zinc)?
(a) The minerals are good conductors of electricity and produce strong induced currents and strong returning magnetic fields.
(b) The minerals absorb the incident magnetic field, indicating their presence by a lack of returning signal.
(c) The minerals produce their own returning magnetic fields.
(d) The minerals attract the incoming magnetic field and reflect it directly above the minerals.

Mayukh Banik

Numerade Educator

Problem 71

Which of the statements below about magnetic induction tomography (MIT) and transcranial magnetic stimulation (TMS), studied in Section $21.5,$ are true?
(a) Both MIT and TMS have source currents in coils, source magnetic fields, and induced currents.
(b) MIT detects the induced magnetic field produced by the induced current, and TMS does not.
(c) MIT provides information directly about the imaged area, whereas TMS disrupts some brain activity, and the disruption is measured in some other way.
(d) a and c only
(e) $a, b,$ and $c$

Anna Zeng

Numerade Educator

Problem 72

Describe all the changes that would occur if the source current were in the direction shown in Figure 21.28 but decreasing instead of increasing.
(a) The induced current would be in the opposite direction.
(b) The induced magnetic field would be in the opposite direction.
(c) The detected current would be in the opposite direction.
(d) $a$ and $b$
(e) $\mathrm{a}, \mathrm{b},$ and $\mathrm{c}$

Mayukh Banik

Numerade Educator

Problem 73

Which of the quantities $B_{\mathrm{ex}}, A,$ or $\theta$ is changing as the fly turns?
(a) $B_{\text {ex }}$
(b) $A$
(c) $\theta$
(d) All of them
(e) None of them

Vishal Gupta

Numerade Educator

Problem 74

Which answer is closest to the magnitude of the flux change?
(a) $1 \times 10^{-4} \mathrm{T} \cdot \mathrm{m}^{2}$
(b) $2 \times 10^{-6} \mathrm{T} \cdot \mathrm{m}^{2}$
(c) $3 \times 10^{-7} \mathrm{T} \cdot \mathrm{m}^{2}$
(d) $5 \times 10^{-8} \mathrm{T} \cdot \mathrm{m}^{2}$

Vishal Gupta

Numerade Educator

Problem 75

Which answer is closest to the induced emf on the tsetse fly coil during the $90^{\circ}$ turn?
(a) $6 \times 10^{-2} \mathrm{V}$
(b) $1 \times 10^{-4} \mathrm{V}$
(c) $4 \times 10^{-6} \mathrm{V}$
(d) $2 \times 10^{-7} \mathrm{V}$

Vishal Gupta

Numerade Educator

Problem 76

Which of the following could double the emf produced when the fly turns $90^{\circ} ?$
(a) Double the number of turns in the coil.
(b) Double the coil's area.
(c) Double the magnitude of the external magnetic field.
(d) Get the tsetse fly to take twice as long to turn.
(e) $a, b,$ and $c$

Vishal Gupta

Numerade Educator