College Physics 2013

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?

Your friend insists that a strong magnetic field is required to induce a current in a coil that has no battery. Describe one experiment that she and you can perform to observe that a strong magnetic field helps induce an electric current and two experiments where no current is induced even with a strong magnetic field. What should you conclude about your friend’s idea?

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 P18.3. (a) Will the ring feel warm if there is constant nonzero current in the solenoid? (b) Will the ring feel warm if the current in the solenoid is alternating? Explain your answers,

To check whether a light bulb 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 P18.4. Explain how or whether each of the following actions can help you determine if the light bulb is ok. (a) Close the switch in circuit A. (b) Keep
the switch in circuit A closed. (c) Open the switch in circuit A.

" Flashlight without batteries A flashlight that operates without batteries is lying on your desk. The light illuminates only when you continuously squecze the flashlight's handle. You also notice that paper clips tend to stick to the outside

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.)

Detect burglars entering windows 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.

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?

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 $\mathrm{P} 18.9$ . Determine the magnetic flux through (a) surface abcd, (b) surfacebcef, and (c) surface adef.

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?

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

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.

You perform experiments using an apparatus that has two insulated wires wrapped around a cardboard tube (Figure P18.4). Determine the direction of the current in the bulb when (a) the switch is closing and the current in loop A is increasing, (b) the switch has just closed and there is a steady current in
loop A, and (c) the switch has just opened and the current in loop A is decreasing.

You have the apparatus shown in Figure P18.14. 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.

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.

"Your friend thinks that an induced magnetic field is always opposite the changing external field that induces an electric current. Provide a detailed description of a situation in which this idca would violate energy conscrvation.

The magnetic flux through three different coils is changing as shown in Figure $P 18.17$ . For each situation, draw a corresponding graph showing qualitatively how the induced emf changes with time

The magnetic flux through three different coils is changing as shown in Figure $P 18.18$ . For each situation, draw a corresponding graph showing quantitatively how the induced emf changes with time.

sA magnetic field passing through two identical coils 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?

Stimulating the brain 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 T in 0.080 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.

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 mag-
net 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 electromagnet is reduced to zero in 1.5 $\mathrm{s}$ , the ammeter in the coil shows a steady reading of 180 $\mathrm{mA}$ . Draw a picture of the experimental setup and determine everything you can about the electromagnet.

You want to use the idea of electromagnetic induction to make the bulb in your small flashlight glow; it glows when the potential difference across it is 1.5 $\mathrm{V}$ . 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.

Breathing monitor An apnea monitor for adults consists of a flexible coil that wraps around the chest (Figure P18.23). When the patient inhales, the chest expands, as does the coil. Earth's $\vec{B}$ field of
$5.0 \times 10^{-5}$ 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 $\mathrm{s}$ .

A bar magnet induces a current in an N-turn coil as the magnet moves closer to it (Figure $P(8.24) .$ The coil's radius is $R \mathrm{cm},$ and the average induced emf across the bulb during the time interval is $\varepsilon$ . (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.

You have a coil of wire with 10 turns each of 1.5 cm radius. You place the plane of the coil perpendicular to a 0.40-Tu B field produced by the poles of an electromagnet (Figure Q18.2). (a) Find the magnitude of the average induced emf in the coil when the magnet is turned off and the field decreases to 0 T in 2.4 s. (b) Is the direction of the induced current in the galvanometer from lead a to b, or from b to a? Explain.

An experimental apparatus has two parallel horizontal metal rails separated by $1.0 \mathrm{m} . \mathrm{A} 2.0-\Omega$ 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 $5.0 \times 10^{-3-\mathrm{T}}$ $\vec{B}$ 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.

Two horizontal metal rails are separated by 1.5 $\mathrm{m}$ and connected at their ends by a $3.0-\Omega$ resistor to form a long, thin U shape. A metal axle with metal wheels on each side rolls along
the rails at a speed of 25 $\mathrm{m} / \mathrm{s}$ . Earth's $\vec{B}$ field has a magnitude of $5.0 \times 10^{-5} \mathrm{T}$ and tilts downward $68^{\circ}$ below the horizontal. Make a list of the physical quantities you can determine using this information and determine two of them.

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.

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

Magnetic field and brain cells 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.

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 clectromagnet 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) 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.

"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 $R(\Omega)$ .

Equation Jeopardy 1 Invent a problem for which the fol- lowing equation might be a solution.
$$
0.01 \mathrm{V}=(100) \frac{(A) \cos 0^{\circ}(0.12 \mathrm{T}-0)}{(1.2 \mathrm{s}-0)}
$$

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

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

Generator for space station 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 $3.0 \times 10^{-7} \mathrm{T}$ . They have a coil that rotates $90^{\circ}$ in 1.2 $\mathrm{s}$ . 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 V. Indicate any assumptions you
made. Is this a feasible way to produce electric energy?

The surface of the coil of wire discussed in Problem 25 is initially oriented perpendicular to the field, as shown in Figure $\mathrm{Q} 18.2 .(\mathrm{a})$ Estimate the magnitude of the average induced emf if the coil is rotated $90^{\circ}$ in 0.050 s in the $0.40-\mathrm{T}$ field. The coil's surface is now parallel to the $\vec{B}$ field. (b) Determine the magnitude of the average induced emf if the coil
is rotated another $90^{\circ}$ in 0.020 $\mathrm{s}$ .

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 $\mathrm{V}$ . 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 by one-fourth while the radius of the coil is reduced by one-half.

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.

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
$\vec{B}$ ficld. If the coil rotates at 400 revolutions per sccond, what must the area of the coil be to develop this emf? Describe any problems with this design (if there are any).

Evaluating a claim 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 mag-
net and coil never touch. Does this lighting system really produce no resistance to riding? Justify your answer.

"The alternator in an automobile produces an emf with a maximum value of 12 $\mathrm{V}$ when the engine is idling at 1000 revolutions per minute (rpm). What is the maximum emf when the engine of the moving car turns at 3000 $\mathrm{rpm}$ ?

A generator has a 100 -turn coil that rotates in a $0.30-\mathrm{T}$ magnitude $\vec{B}$ field at a frequency of 80 $\mathrm{Hz}$ (80 rotations per second) causing a peak emf of 38 $\mathrm{V}$ . (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.

A 10 -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 $\mathrm{s} .(\mathrm{c})$ Plot these emf-versus-time data on a graph and connect the points with a smooth curve. What is the shape of the curve?

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?

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.

A 9.0 - 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.

You are fixing a transformer for a toy truck that uses an $8.0-\mathrm{V}$ emf 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 $240-\mathrm{V}$ source, what emf would be across the secondary coil?

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 electri-
cal resistance of the loop?

lce skater's flashing belt 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?

Ha mmerhead shark A hammerhead shark (Figure P18.51) 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 $30^{\circ} \times 10^{-5}$ The direction of the shark's travel. Determine the potential difference between the two sides of the shark's head.

Car braking system 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 brake the car? Explain.

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.

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 $0.20-\mathrm{kg}$ 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. ( $(\mathrm{c})$ Determine the final constant speed of the falling bar (d) Is this process realistic? Explain.

Designing a sparker Your friend decides to use a device that converts some mechanical energy into the production of a spark to ignite lighter fluid. Use the information and the questions below to decide whether his sparker will work. The sparker has a coil connected across a very short gap $(0.1 \mathrm{mm})$ between the ends of the wire in the coil. (a) Estimate the potential difference needed across this gap to cause dielectric breakdown (a spark) to ignite the fumes from the
wick. Dielectric breakdown occurs when the magnitude of the E field is 3 * 106 V/m or greater. (b) Estimate, based on mechanical properties, the shortest time interval that you think a person can push a small magnet from several centimeters away to the surface of a coil. (c) As the magnet is pushed
toward the coil, the field in the coil increases and causes an induced emf. If the magnetic flux inside one loop increases by 10-6 T # m2 as the magnet moves forward, how many coil turns are needed to produce the emf to cause a spark? Is this a reasonable lighter system?

You have a 12 -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.

Design a burglar alarm You decide to build your own burglar alarm. Your window frames are wood, so you decide to fit the sides with metal sliders and the bottom with metal strips. These changes will turn the window area into a metal loop whose size changes as the window opens. Your idea is that an electric current will be induced in this loop as the window opens in Earth’s magnetic field. The current can set off
an alarm if a burglar enters. How feasible is your idea?

You want to build a generator for a multi-day canoe trip. You have a fairly large permanent magnet, some wire, and a light- bulb. 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.)

Free energy from power line While on a camping trip, you decide to get some free electric energy. A power line is 12 m above the ground and carries an alternating current. You place a 0.50 m * 3.0 m coil with 100 turns below the wire so it lies with the 3.0-m side on the ground. The coil is connected to a light bulb. (a) Will the light bulb glow? (b) Indicate in a drawing the orientation of the coil relative to the power line so that a maximum changing flux passes through the coil. (c) If the cur- rent in the power line decreases from 200 A to 0 A in 1/240 s, what is the average emf induced in the coil? [Hint: Determine the
B field produced by the long straight power line (see Chap ter 17)]. Describe any assumptions that you make.

A sparker used to ignite lighter fluid in a barbeque grill is shown in Figure P18.60. 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-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.

MRI power failure Jose needs an MRI (mag-netic resonance imaging) scan. During the exam, Jose lies
in a region of a very strong $1.5-$ T magnetic field that points down into his chest from above. A sudden power failure causes the power supply for the magnet to shut down, reducing the magnetic field from 1.5 $\mathrm{T}$ to 0 $\mathrm{T}$ in 0.50 $\mathrm{s}$ . Consequently, the $\vec{B}$ field through Jose's 0.3 $\mathrm{m}$ by 0.4$\cdot \mathrm{m}$ chest decreases. The conductive fluid tissue inside his body along the edge 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 $B$ 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?

Magstripe reader 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 mags tripe magnetic field changes at a constant rate of 500 mT/ms as the region between two tiny magnets on the stripe passes the coil. The reader coil is 2.0 mm in diameter and has 5000 turns.

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 $B I y$ .

The Tower of Terror ride Figure 18.10 shows Tower of Terror vehicle near the vertical end of its ride. (a) Is its 161-km/h speed what you would expect of an object after a 115-m fall? Explain. (b) Estimate the time interval for the free-fall part of its trip. (c) Estimate the average acceleration of the vehicle while stopping due to its magnetic braking.

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 nearbyconductive layer.
(b) The induced current is greater if the soil is moist andconductive.
(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) b and c

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 ionscompared 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 electricalconductor than loose, dry topsoil.

Why is MIT used to search noninvasively for mineral deposits (iron, copper, zinc)?
(a) The minerals are good conductors of clectricity 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.

Which of the statements below about magnetic induction tomography (MIT) and transcranial magnetic stimulation .(TMS), studied in Section $18.6,$ 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 conly $\quad(\text { e })$ a, b, and $c$

Describe all the changes that would occur if the source current were in the direction shown in Figure 18.20 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 $\quad$ (e) $a, b,$ and $c$

Which of the quantities $B_{c x}, A,$ or $\theta$ is changing as the fly turns?
$$
\begin{array}{ll}{\text { (a) } B_{x}} & {\text { (b) } A} & {(c) \theta} \\ {\text { (d) All of them }} & {\text { (e) None of them }}\end{array}
$$

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

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

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