Essential University Physics

Richard Wolfson

Chapter 27

Electromagnetic Induction - all with Video Answers

Educators

Chapter Questions

Problem 1

In Fig. $27.35,$ a bar magnet moves toward a conducting ring. What's the direction of the induced current in the ring? (FIGURE CAN'T COPY)

Mohammad Amin

Mohammad Amin

Numerade Educator

Problem 2

Figure 27.36 shows two concentric conducting loops, the outer connected to a battery and a switch. The switch is initially open. It's then closed, left closed for a while, and then reopened. Describe the currents in the inner loop during the entire procedure. (FIGURE CAN'T COPY)

Mohammad Amin

Numerade Educator

Problem 3

Fluctuations in Earth's magnetic field due to changing solar activity can wreak havoc with communications, even those using underground cables. How is this possible?

Mohammad Amin

Numerade Educator

Problem 4

Chapter 26 stated that a static magnetic field cannot change the energy of a charged particle. Is this true of a changing magnetic field? Discuss.

Mohammad Amin

Numerade Educator

Problem 5

Can an induced electric field exist in the absence of a conductor?

Mohammad Amin

Numerade Educator

Problem 6

A car battery has a $12-\mathrm{V}$ emf, yet energy from the battery provides the 30,000 -V spark that ignites the gasoline. How is this possible?

Mohammad Amin

Numerade Educator

Problem 7

You have a fixed length of wire to wind into an inductor. Will you get more inductance if you wind a short coil with large diameter, or a long coil with small diameter?

Mohammad Amin

Numerade Educator

Problem 8

In a popular demonstration of induced emf, a lightbulb is connected across a large inductor in an $R L$ circuit, as shown in Fig. $27.37 .$ When the switch is opened, the bulb flashes brightly and may even burn out. Why? (FIGURE CAN'T COPY)

Mohammad Amin

Numerade Educator

Problem 9

List some similarities and differences between inductors and capacitors.

Mohammad Amin

Numerade Educator

Problem 10

A $1-$ H inductor carries $10 \mathrm{A},$ and a $10-\mathrm{H}$ inductor carries $1 \mathrm{A}.$ Which contains more stored energy?

Mohammad Amin

Numerade Educator

Problem 11

It takes work to push two bar magnets together with like poles facing. Where does this energy go?

Mohammad Amin

Numerade Educator

Problem 12

A small magnet is dropped into each of two hollow vertical tubes of equal length, one made of copper and one of aluminum. Does it take longer for the magnet to fall through the aluminum tube or the copper tube, or does it take the same amount of time for each? (Hint: Consult Table 24.1.)

Vishal Gupta

Numerade Educator

Problem 13

Figures $27.1 b$ and 27.2 actually describe the same situation, just from the viewpoints of two different inertial reference frames. In Fig. $27.2,$ in the reference frame of the magnet, you can think of the induced current as arising from the magnetic force on the electrons in the coil (motional emf). From the coil's reference frame (Fig. $27.1 b$ ), how would you describe the origin of the induced current? (This comparison played an important role in Einstein's thinking about relativity, and the phrase "the reciprocal electrodynamic action of a magnet and a conductor" appears in the second sentence of Einstein's 1905 paper introducing the special theory of relativity; more in Chapter $33 .$ )

Mohammad Amin

Numerade Educator

Problem 14

Show that the volt is the SI unit for the rate of change of magnetic flux, making Faraday's law dimensionally correct. Your result also shows why the unit of flux itself can be expressed as $\mathrm{V} \cdot \mathrm{s}.$

Mohammad Amin

Numerade Educator

Problem 15

Find the magnetic flux through a 5.0 -cm-diameter circular loop oriented with the loop normal at $36^{\circ}$ to a uniform $75-\mathrm{mT}$ magnetic field.

Mohammad Amin

Numerade Educator

Problem 16

A circular wire loop $45 \mathrm{cm}$ in diameter has resistance $120 \Omega$ and lies in a horizontal plane. A uniform magnetic field points vertically downward, and in 25 ms it increases linearly from $5.0 \mathrm{mT}$ to $55 \mathrm{mT.}$ Find the magnetic flux through the loop at (a) the beginning and (b) the end of the 25 -ms period. (c) What's the loop current during this time? (d) Which way does this current flow?

Mohammad Amin

Numerade Educator

Problem 17

A conducting loop of area $240 \mathrm{cm}^{2}$ and resistance $12 \Omega$ is perpendicular to a spatially uniform magnetic field and carries a $320-\mathrm{mA}$ induced current. At what rate is the magnetic field changing?

Mohammad Amin

Numerade Educator

Problem 18

The magnetic field inside a 23 -cm-diameter solenoid is increasing at $2.4 \mathrm{T} / \mathrm{s}$. How many turns should a coil wrapped around the outside of the solenoid have so that the emf induced in the coil is $15 \mathrm{V} ?$

Mohammad Amin

Numerade Educator

Problem 19

Find the self-inductance of a 1500 -turn solenoid $55 \mathrm{cm}$ long and $4.0 \mathrm{cm}$ in diameter.

Mohammad Amin

Numerade Educator

Problem 20

The current in an inductor is changing at $110 \mathrm{A} / \mathrm{s}$ and the inductor emf is 45 V. What's the self-inductance?

Mohammad Amin

Numerade Educator

Problem 21

A 1.9 -A current is flowing in a 22 - H inductor. A switch opens, interrupting the current in 1.0 ms. Find the induced emf in the inductor.

Mohammad Amin

Numerade Educator

Problem 22

Your little sister is building a radio from scratch. Plans call for a $450-\mu \mathrm{H}$ inductor wound on a cardboard tube. She brings you the tube from a toilet-paper roll ( $12 \mathrm{cm}$ long, $4.0 \mathrm{cm}$ diameter), and asks how many turns she should wind on the full length of the tube. Your answer?

Mohammad Amin

Numerade Educator

Problem 23

What inductance should you put in series with a $150-\Omega$ resistor to give a time constant of $2.2 \mathrm{ms} ?$

Mohammad Amin

Numerade Educator

Problem 24

The current in a series $R L$ circuit increases to $20 \%$ of its final value in $3.1 \mu \mathrm{s} .$ If $L=1.8 \mathrm{mH},$ what's the resistance?

Mohammad Amin

Numerade Educator

Problem 25

How much energy is stored in a $5.0-\mathrm{H}$ inductor carrying $35 \mathrm{A} ?$

Vishal Gupta

Numerade Educator

Problem 26

What's the current in a 24 -mH inductor storing $75 \mu$ J of energy?

Mohammad Amin

Numerade Educator

Problem 27

A 220 -mH inductor carries 350 mA. How much energy must be supplied to the inductor in raising the current to 850 mA?

Mohammad Amin

Numerade Educator

Problem 28

A 1250 -turn solenoid $23.2 \mathrm{cm}$ long and $1.58 \mathrm{cm}$ in diameter carries 165 mA. How much magnetic energy does it contain?

Mohammad Amin

Numerade Educator

Problem 29

Show that the quantity $B^{2} / 2 \mu_{0}$ has the units of energy density.

Farhanul Hasan

Numerade Educator

Problem 30

The world's strongest magnet that can produce a sustained field is a 45-T device at the National High Magnetic Field Laboratory in Florida. What's the corresponding magnetic-energy density?

Mohammad Amin

Numerade Educator

Problem 31

Find the magnetic-field strength in a region where the magneticenergy density is $7.8 \mathrm{J} / \mathrm{cm}^{3}.$

Mohammad Amin

Numerade Educator

Problem 32

The induced electric field $12 \mathrm{cm}$ from the axis of a 10 -cm-radius solenoid is $45 \mathrm{V} / \mathrm{m} .$ Find the rate of change of the solenoid's magnetic field.

Mohammad Amin

Numerade Educator

Problem 33

Find an expression for the electric-field strength inside the solenoid of Example $27.10,$ a distance $r$ from the axis.

Mohammad Amin

Numerade Educator

Problem 34

A conducting loop of area $A$ and resistance $R$ lies at right angles to a spatially uniform magnetic field. At time $t=0,$ the magnetic field and loop current are both zero. Subsequently, the current increases according to $I=b t^{2},$ where $b$ is a constant with units A/s $^{2} .$ Find an expression for the magnetic-field strength as a function of time.

Vishal Gupta

Numerade Educator

Problem 35

A conducting loop with area $0.15 \mathrm{m}^{2}$ and resistance $6.0 \Omega$ lies in the $x-y$ plane. A spatially uniform magnetic field points in the z-direction. The field varies with time according to $B_{z}=a t^{2}-b$ where $a=2.0 \mathrm{T} / \mathrm{s}^{2}$ and $b=8.0 \mathrm{T} .$ Find the loop current (a) at $t=3.0 \mathrm{s}$ and $(\mathrm{b})$ when $B_{z}=0.$

Mohammad Amin

Numerade Educator

Problem 36

A square wire loop of side $l$ and resistance $R$ is pulled with constant speed $v$ from a region of no magnetic field until it's fully inside a region of constant, uniform magnetic field $\vec{B}$ perpendicular to the loop plane. The boundary of the field region is parallel to one side of the loop. Find an expression for the total work done by whatever is pulling the loop.

Mohammad Amin

Numerade Educator

Problem 37

A 5 -turn coil $1.0 \mathrm{~cm}$ in diameter is rotated at $10 \mathrm{rev} / \mathrm{s}$ about an axis perpendicular to a uniform magnetic field. A voltmeter connected to the coil through rotating contacts reads a peak value $360 \mu \mathrm{V}$. What's the magnetic-field strength?

Vishal Gupta

Numerade Educator

Problem 38

A magnetic field is given by $\vec{B}=B_{0}\left(x / x_{0}\right)^{2} \hat{k},$ where $B_{0}$ and $x_{0}$ are constants. Find an expression for the magnetic flux through a square of side $2 x_{0}$ that lies in the $x$ -y plane with one corner at the origin and sides coinciding with the positive $x$ - and $y$ -axes.

Farhanul Hasan

Numerade Educator

Problem 39

A square wire loop $3.0 \mathrm{m}$ on a side is perpendicular to a uniform 2.0-T magnetic field. A 6-V lightbulb is in series with the loop, as shown in Fig. $27.38 .$ The magnetic field is reduced steadily to zero over time $\Delta t .$ (a) Find $\Delta t$ such that the bulb will shine at full brightness. (b) Which way will the loop current flow? (FIGURE CAN'T COPY)

Ajay Singhal

Numerade Educator

Problem 40

In Example 27.2 take $a=1.0 \mathrm{cm}, w=3.5 \mathrm{cm},$ and $l=6.0 \mathrm{cm}$ Suppose the rectangular loop is a conductor with resistance $50 \mathrm{m} \Omega,$ and the current $I$ in the long wire is increasing at $25 \mathrm{A} / \mathrm{s}$ Find the induced current in the loop. What's its direction?

Farhanul Hasan

Numerade Educator

Problem 41

A 2000 -turn solenoid is $2.0 \mathrm{m}$ long and $15 \mathrm{cm}$ in diameter. The solenoid current is increasing at $1.0 \mathrm{kA} / \mathrm{s} .$ (a) Find the current in a 10 -cm-diameter wire loop with resistance $5.0 \Omega$ lying inside the solenoid and perpendicular to the solenoid axis. (b) Repeat for a similarly oriented 25 -cm-diameter loop with the same resistance, lying entirely outside the solenoid.

Sheh Lit Chang

University of Washington

Problem 42

A stent is a cylindrical tube, often made of metal mesh, that's inserted into a blood vessel to overcome a constriction. It's sometimes necessary to heat the stent after insertion to prevent cell growth that could cause the constriction to recur. One method is to place the patient in a changing magnetic field, so that induced currents heat the stent. Consider a stainless-steel stent $12 \mathrm{mm}$ long by $4.5 \mathrm{mm}$ in diameter, with total resistance $41 \mathrm{m} \Omega .$ Treating the stent as a wire loop in the optimum orientation, find the rate of change of magnetic field needed for a heating power of $250 \mathrm{mW}.$

Vishal Gupta

Numerade Educator

Problem 43

A uniform magnetic field is given by $\vec{B}=b t \hat{k},$ where $b=$ 0.35 T/s. Find the induced current in a conducting loop with area $240 \mathrm{cm}^{2}$ and resistance $0.20 \Omega$ that lies in the $x-y$ plane. In what direction is the current, as viewed from the positive z-axis?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 44

You're an electrical engineer designing an alternator (the generator that charges a car's battery). Mechanical engineers specify a 10-cm-diameter rotating coil, and you determine that you can fit 250 turns in this coil. To charge a $12-\mathrm{V}$ battery, you need a peak output of $14 \mathrm{V}$ when the alternator is rotating at $1200 \mathrm{rpm}$. What do you specify for the alternator's magnetic field?

Mohammad Amin

Numerade Educator

Problem 45

A generator consists of a rectangular coil $75 \mathrm{cm}$ by $1.3 \mathrm{m},$ spinning in a 0.14 -T magnetic field. If it's to produce a $60-\mathrm{Hz}$ alternating emf with peak value $6.7 \mathrm{kV},$ how many turns must it have?

Mohammad Amin

Numerade Educator

Problem 46

Figure 27.39 shows a pair of parallel conducting rails a distance $l$ apart in a uniform magnetic field $\vec{B}$. A resistor $R$ is connected across the rails, and a conducting bar of negligible resistance is being pulled along the rails with velocity $\vec{v}$ to the right. (a) What direction is the current in the resistor? (b) At what rate does the agent pulling the bar do work? (FIGURE CAN'T COPY)

Mohammad Amin

Numerade Educator

Problem 47

The resistor in Problem 46 is replaced by an ideal voltmeter. (a) To which rail should the positive meter terminal be connected if it's to indicate a positive voltage? (b) At what rate does the agent pulling the bar do work?

Mohammad Amin

Numerade Educator

Problem 48

A battery of emf $\mathcal{E}$ is inserted in series with the resistor in Fig. $27.39,$ with its positive terminal toward the top rail. The bar is initially at rest, and now nothing's pulling it. (a) Describe the bar's subsequent motion. (b) The bar eventually reaches a constant speed. Why? (c) What is that constant speed, in terms of the magnetic field, the battery emf, and the rail spacing $l ?$ Does the resistance $R$ affect the final speed? If not, what role does it play?

Ajay Singhal

Numerade Educator

Problem 49

In Fig. $27.39,$ take $l=10 \mathrm{cm}, B=0.50 \mathrm{T}, R=4.0 \Omega,$ and $v=2.0 \mathrm{m} / \mathrm{s} .$ Find $(\mathrm{a})$ the current in the resistor, $(\mathrm{b})$ the magnetic force on the bar, (c) the power dissipation in the resistor, and
(d) the mechanical power supplied by the agent pulling the bar. Compare your answers to parts (c) and (d).

Mohammad Amin

Numerade Educator

Problem 50

The magnetic field inside a solenoid of circular cross section is given by $\vec{B}=b t \hat{k},$ where $b=2.1$ T/ms. At time $t=0.40 \mu \mathrm{s},$ a proton is inside the solenoid at $x=5.0 \mathrm{cm}, y=z=0,$ and is moving with velocity $\vec{v}=4.8 \hat{\jmath} \mathrm{Mm} / \mathrm{s} .$ Find the electromagnetic force on the proton.

Dominador Tan

Numerade Educator

Problem 51

An electron is inside a solenoid, $28 \mathrm{cm}$ from the axis. It experiences a 1.3 -fN electric force. At what rate is the solenoid's magnetic field changing?

Mohammad Amin

Numerade Educator

Problem 52

During lab, you're given a circular wire loop of resistance $R$ and radius $a$ with its plane perpendicular to a uniform magnetic field. You're supposed to increase the field strength from $B_{1}$ to $B_{2}$ and measure the total charge that moves around the loop. Your lab partner claims that the details of how you vary the field will make a difference in the total charge; your hunch is that it won't. By integrating the loop current over time, determine who's right.

Mohammad Amin

Numerade Educator

Problem 53

A flip coil is used to measure magnetic fields. It's a small coil placed with its plane perpendicular to a magnetic field, and then flipped through $180^{\circ} .$ The coil is connected to an instrument that measures the total charge $Q$ that flows during this process. If the coil has $N$ turns, area $A$, and resistance $R,$ show that the field strength is $B=Q R / 2 N A.$

Sheh Lit Chang

University of Washington

Problem 54

The current in a series $R L$ circuit rises to half its final value in $7.6 \mathrm{s}$ What's the time constant?

Mohammad Amin

Numerade Educator

Problem 55

In a series $R L$ circuit like Fig. $27.23 a, \mathcal{E}_{0}=45 \mathrm{V}, R=3.3 \Omega$ and $L=2.1 \mathrm{H} .$ If the current is $9.5 \mathrm{A},$ how long has the switch been closed?

Farhanul Hasan

Numerade Educator

Problem 56

In Fig. $27.23 a,$ take $R=2.5 \mathrm{k} \Omega$ and $\mathcal{E}_{0}=50 \mathrm{V} .$ When the switch is closed, the current through the inductor rises to $10 \mathrm{mA}$ in $30 \mu$ s. Find (a) the inductance and (b) the current in the circuit after many time constants.

Farhanul Hasan

Numerade Educator

Problem 57

How long does it take to dissipate $90 \%$ of the magnetic energy in Example $27.9 ?$

Farhanul Hasan

Numerade Educator

Problem 58

A series $R L$ circuit like Fig. $27.23 a$ has $\mathcal{E}_{0}=60 \mathrm{V}, R=22 \Omega$ and $L=1.5 \mathrm{H} .$ Find the rate of change of the current (a) immediately after the switch is closed and (b) 100 ms later.

Farhanul Hasan

Numerade Educator

Problem 59

You're a safety engineer reviewing plans for a university's new high-rise dorm. The elevator motors draw $20 \mathrm{A}$ and behave electrically like $2.5-\mathrm{H}$ inductors. You're concerned about dangerous voltages developing across the switch when a motor is turned off, and you recommend that a resistor be wired in parallel with each motor. (a) What should be the resistance in order to limit the emf to $100 \mathrm{V} ?$ (b) How much energy will the resistor dissipate?

Farhanul Hasan

Numerade Educator

Problem 60

In Fig. $27.26,$ take $\mathcal{E}_{0}=12 \mathrm{V}, R=2.7 \Omega,$ and $L=20 \mathrm{H} .$ Initially the switch is in position $B$ and there's no current anywhere. At $t=0$ the switch is thrown to position $A,$ and at $t=10 \mathrm{s}$ it's returned to $B$. Find the inductor current at (a) $t=5.0 \mathrm{s}$ and (b) $t=15 \mathrm{s}.$

Farhanul Hasan

Numerade Educator

Problem 61

In Fig. $27.40,$ take $\mathcal{E}_{0}=12 \mathrm{V}, R_{1}=4.0 \Omega, R_{2}=8.0 \Omega,$ and $R_{3}=2.0 \Omega .$ Find current $I_{2}$ (a) immediately after the switch is first closed and (b) a long time later. (c) After a long time, the switch is reopened. Now what's $I_{2} ?$ (FIGURE CAN'T COPY)

Dominador Tan

Numerade Educator

Problem 62

A battery, switch, resistor, and inductor are connected in series. When the switch is closed, the current rises to half its steadystate value in 1.0 ms. How long does it take for the magnetic energy in the inductor to rise to half its steady-state value?

Farhanul Hasan

Numerade Educator

Problem 63

When a nonideal $1.0-\mathrm{H}$ inductor is short-circuited, its magnetic energy drops to one-fourth of its original value in 3.6 s. What is its resistance?

Farhanul Hasan

Numerade Educator

Problem 64

Your hospital is installing a new MRI scanner using a $3.5-\mathrm{H}$ superconducting solenoid carrying $1.8 \mathrm{kA} .$ Copper is embedded in the coils to carry the current in the event of a quench (see Example $27.9) .$ As safety officer, you're to specify (a) the maximum resistance that will limit power dissipation to $100 \mathrm{kW}$ immediately after a loss of superconductivity and (b) the time it will take the power to drop to $50 \mathrm{kW}$. What specs do you give?

Farhanul Hasan

Numerade Educator

Problem 65

A neutron star's magnetic field is about $10^{8}$ T. Consult Appendix $C$ to compare the energy density in this field with that of (a) gasoline and (b) pure uranium-235 (mass density $19 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$ ).

Farhanul Hasan

Numerade Educator

Problem 66

A single-turn loop of radius $R$ carries current $I .$ How does the magnetic-energy density at the loop center compare with that of a long solenoid of the same radius, carrying the same current, and consisting of $n$ turns per unit length?

Farhanul Hasan

Numerade Educator

Problem 67

A wire of radius $R$ carries current $I$ distributed uniformly over its cross section. Find an expression for the total magnetic energy per unit length within the wire.

Farhanul Hasan

Numerade Educator

Problem 68

(a) Use Equation 27.8 to write an expression for the resistor's power dissipation as a function of time, and (b) integrate from $t=0$ to $t=\infty$ to show that the total energy dissipated is equal to the energy initially stored in the inductor.

Farhanul Hasan

Numerade Educator

Problem 69

An electric field and a magnetic field have the same energy density. Find an expression for the ratio $E / B$ and evaluate this ratio numerically. What are its units? Is your answer close to any of the fundamental constants listed inside the front cover?

Farhanul Hasan

Numerade Educator

Problem 70

A rectangular conducting loop of resistance $R,$ mass $m,$ and width $w$ falls into a uniform magnetic field as shown in Fig. 27.41
(a) Explain why the loop eventually reaches a terminal speed.
(b) Find an expression for the terminal speed.
(FIGURE CAN'T COPY)

Farhanul Hasan

Numerade Educator

Problem 71

A conducting disk with radius $a$, thickness $h,$ and resistivity $\rho$ is inside a solenoid of circular cross section, its axis coinciding with the solenoid axis. The magnetic field in the solenoid is given by $B=b t,$ where $b$ is a constant. Find expressions for (a) the current density in the disk as a function of the distance $r$ from the disk center and (b) the power dissipation in the entire disk. (Hint: Consider the disk as consisting of infinitesimal conducting loops.)

Jerrah Biggerstaff

Jerrah Biggerstaff

Numerade Educator

Problem 72

A long, straight coaxial cable consists of two thin, tubular conductors, the inner of radius $a$ and the outer of radius $b$. Current $I$ flows out along one conductor and back along the other. Show that the self-inductance per unit length of the cable is $\frac{\mu_{0}}{2 \pi} \ln (b / a)$

Farhanul Hasan

Numerade Educator

Problem 73

The table below shows the current in a circuit like that of Fig. $27.26,$ where a current has been established with the switch in position $A,$ and then it's thrown to position $B$ at time $t=0$ The resistance is $180 \Omega .$ Determine an appropriate function of current that, when plotted against time, should produce a straight line. Make your plot, determine a best-fit line, and use its slope to find the inductance in the circuit.
$$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Time (ms) } & 0 & 20.0 & 40.0 & 60.0 & 80.0 & 100.0 \\ \hline \text { Current (mA) } & 66.5 & 23.0 & 9.15 & 3.56 & 1.50 & 0.450 \\ \hline \end{array}$$

Farhanul Hasan

Numerade Educator

Problem 74

A circular wire loop of radius $a$ and resistance $R$ is pulled with constant speed $v$ into a uniform magnetic field $B .$ The loop is perpendicular to the field, and it begins entering the field at time $t=0 .$ Find an expression for the current in the loop from $t=0$ until the loop is fully immersed in the field.

Dominador Tan

Numerade Educator

Problem 75

The bar in Problem 46 has mass $m$ and is initially at rest. A constant force $F$ to the right is applied to the bar. Formulate Newton's second law for the bar, and find its velocity as a function of time.

Farhanul Hasan

Numerade Educator

Problem 76

Use the node and loop laws to determine the current in $R_{2}$ as a function of time after the switch is closed in Conceptual Example 27.1.

Dominador Tan

Numerade Educator

Problem 77

(a) Find the magnetic-energy density as a function of radial distance for the coaxial cable of Problem $72,$ and integrate over the volume between the conductors to show that the total energy per unit length of the cable is given by $\left(\mu_{0} I^{2} / 4 \pi\right) \ln (b / a).$
(b) Use the expression $U=\frac{1}{2} L I^{2}$ to find the inductance per unit length, and show that your result agrees with that of Problem 72.

Farhanul Hasan

Numerade Educator

Problem 78

You and your roommate are headed to Cancún for spring break. Your roommate, who has had only high school physics, has read that an emf can be induced in the wings of an airplane and wonders whether this would give enough voltage to power a portable music player. What's your answer? (Assume that the wingspan of your 747 is $60 \mathrm{m},$ the plane is flying at 600 mph, and Earth's magnetic field is $0.3 \mathrm{G} .$ )

Farhanul Hasan

Numerade Educator

Problem 79

One way to measure blood flow when blood vessels are exposed during surgery is to use an electromagnetic flowmeter. This device surrounds the blood vessel with an electromagnet, creating a magnetic field perpendicular to the blood flow. since blood is a modest conductor, a motional emf develops across the blood vessel. Given vessel diameter $d$, magnetic field $B$, and voltage $V$ measured across the vessel, show that the volume blood flow is given by $\pi d^{2} V / 4 B d.$

Farhanul Hasan

Numerade Educator

Problem 80

Clever farmers with power lines crossing their land have been known to steal power by stringing wire near the power line and making use of the induced current. At least one such crime went to court and resulted in a conviction- despite the defense's claim that the defendant didn't touch the lines. Figure 27.42 shows a possible crime scene, with a rectangular wire loop mounted in a vertical plane beneath a power line. The power line carries a current of $10^{4} \mathrm{A}$, alternating sinusoidally at $60 \mathrm{Hz}$. (FIGURE CAN'T COPY)
If the loop were mounted in a horizontal rather than vertical plane at the same distance from the power line, the induced emf would
a. increase slightly.
b. decrease slightly.
c. remain the same.
d. become essentially zero.

Farhanul Hasan

Numerade Educator

Problem 81

Clever farmers with power lines crossing their land have been known to steal power by stringing wire near the power line and making use of the induced current. At least one such crime went to court and resulted in a conviction- despite the defense's claim that the defendant didn't touch the lines. Figure 27.42 shows a possible crime scene, with a rectangular wire loop mounted in a vertical plane beneath a power line. The power line carries a current of $10^{4} \mathrm{A}$, alternating sinusoidally at $60 \mathrm{Hz}$. (FIGURE CAN'T COPY)
If the loop's vertical dimension were doubled by extending it toward the power line (dashed line in Fig. 27.42 ), the induced emf would
a. double.
b. quadruple.
c. more than double but not quadruple.
d. increase but not quite double.

Farhanul Hasan

Numerade Educator

Problem 82

Clever farmers with power lines crossing their land have been known to steal power by stringing wire near the power line and making use of the induced current. At least one such crime went to court and resulted in a conviction- despite the defense's claim that the defendant didn't touch the lines. Figure 27.42 shows a possible crime scene, with a rectangular wire loop mounted in a vertical plane beneath a power line. The power line carries a current of $10^{4} \mathrm{A}$, alternating sinusoidally at $60 \mathrm{Hz}$. (FIGURE CAN'T COPY)
Suppose the same crime were committed in Europe, where the standard frequency is $50 \mathrm{Hz}$. Assuming everything else about the situation were the same, the induced emf would
a. be greater.
b. be less.
c. be unchanged.
d. depend on the nature of the energy source.

Farhanul Hasan

Numerade Educator

Problem 83

Clever farmers with power lines crossing their land have been known to steal power by stringing wire near the power line and making use of the induced current. At least one such crime went to court and resulted in a conviction- despite the defense's claim that the defendant didn't touch the lines. Figure 27.42 shows a possible crime scene, with a rectangular wire loop mounted in a vertical plane beneath a power line. The power line carries a current of $10^{4} \mathrm{A}$, alternating sinusoidally at $60 \mathrm{Hz}$. (FIGURE CAN'T COPY)
When this crime occurs,
a. more fuel must be consumed at the power plant supplying the line.
b. the power company does not suffer any economic damage.
c. the power company can't determine that it's being robbed without an on-site inspection.
d. there's no power left for customers further down the line.

Farhanul Hasan

Numerade Educator