Magnetic Fields and Electromagnetism 415NEL

8.58.5Electromagnetic InductionThe principle of electromagnetic induction has a wide variety of applications: it is usedin the continent-wide infrastructure that distributes our electric power, in automobiles,at some traffic lights, in security systems, in computer hard drives, and even in amuse-ment-park rides.

As we have seen, a steady electric current (a steady stream of electric charges) pro-duces a steady magnetic field. If a stream of electric charges can cause a magnetic field,then can a magnetic field cause such a stream? It was first thought that a steady magneticfield would produce a steady electric current, but experiments quickly established thisto be false. Faraday investigated this very problem and discovered that the way in whicha magnetic field can produce a current is more subtle.

Faraday first used a solenoid around a wooden core, connected in series with a switchand a powerful battery to form a so-called “primary” circuit. He added a “secondary” cir-cuit, consisting of a second solenoid around the same wooden core, wired in series with agalvanometer configured as an ammeter, or current meter (Figure 1). Closing the switch

induced a weak, short-lived current in the secondary circuit, as the galvanometer needleshowed, but only for a very short time. Once the current dropped back to zero in the sec-ondary circuit, no other current was produced, in spite of the constant current in the pri-mary circuit. When the primary current was switched off, a small current was induced inthe opposite direction in the secondary circuit, again only for a short time (Figure 2).

To improve his results, Faraday built a new device (now called “Faraday’s ring”), whichutilized an iron ring to increase the magnetic field inside the solenoids (Figure 3). Thecurrents were large enough to be easily apparent but still found to occur only when thecurrent was being switched on or off. How were the currents to be explained?

When the current is steady in the primary circuit, the magnetic field in the solenoidis constant over time. In particular, the magnetic field at each point around and in thesecondary coil is constant. No current is induced in the secondary circuit. When theprimary circuit is turned on, the magnetic field in the secondary solenoid changes veryquickly from zero to some maximum value, causing a current. When the primary circuitis turned off, the magnetic field in the secondary solenoid changes from the maximum

secondary coil

primary coil

wooden core galvanometer

switch

battery

Figure 1Faraday’s first induction apparatus. There are two separate circuits. Charges do not pass from the primary circuit into the secondary circuit.

Primary circuitis turned on.

Primary circuitis turned off.

t (s)

I (m

A)

Current in Secondary circuit

Figure 2Only when the primary circuit isturned on and off is a currentinduced in the secondary circuit.There is no current in the secondarycircuit when the current in the pri-mary circuit is constant. The plotshows the two currents to be inopposite directions.

primary

ironcore

secondary

I

Figure 3Faraday’s iron ring. Even though themagnetic fields are stronger than inFaraday’s first apparatus, aninduced current is produced in thesecondary circuit only when the pri-mary circuit is turned on or off,changing the magnetic field.

416 Chapter 8 NEL

value to zero, causing a current in the opposite direction. The key is this: in each case themagnetic field is changing when the current is induced in the secondary circuit. A con-stant magnetic field, even a large one, induces no current at all.

Faraday combined all his observations into the law of electromagnetic induction.

Law of Electromagnetic InductionAn electric current is induced in a conductor whenever the magnetic field in the region of the conductor changes with time.

S NS

v

0

��

S N

v = 0

0

S NS

v

0

��

Figure 4(a) When the S-pole is pushed into

the coil, a current (registeredhere indirectly, by a potentialdifference across oscilloscopeterminals) is produced in thecoil.

(b) When the magnet stops, thecurrent drops to zero.

(c) Removing the magnet causes a current in the opposite direction.

(d) When the magnet stopsmoving, the current againdrops to zero.

S N

v = 0

0

(a) (b) (c) (d)

drive shaft

magnet

sensingcoil

microprocessor

servo controlmechanismthrottle/fuel injector

Figure 5Rotating magnets induce briefpulses of current in a loop con-nected to a microprocessor in acruise-control device. Similar meas-urement devices are used for ABS(the automatic/anti-lock brakingsystem) and traction control on indi-vidual halves of the axle, or onwheels.

You can demonstrate Faraday’s law of electromagnetic induction by plunging a barmagnet into a solenoid connected to a galvanometer (configured as an ammeter) or toan oscilloscope, as shown in Figure 4. (The oscilloscope does not directly indicate a cur-rent. It does, however, indicate a potential difference in the secondary coil, caused bythe changing magnetic field and driving the flow of charges.) As the S-pole enters the sole-noid, the magnetic field in the region of the conductor changes and a current is inducedin the circuit. When the magnet comes to rest, no current is present. When the magnetis withdrawn, a current is induced in the opposite direction, falling to zero as the magnetcomes to rest.

The maximum current measured in such a demonstration is larger if the magnet ismoved faster, if a stronger magnet is used, or if the coil has more turns. A current isproduced even if the magnet is held stationary and the coil moved around it. We con-clude, as Faraday did, that the current is produced by a changing magnetic field and thegreater the change, the larger the induced current.

Faraday’s law is applied in some automobile cruise-control devices, which maintainthe speed of a vehicle (Figure 5). Two magnets are attached to opposite sides of the drive

Magnetic Fields and Electromagnetism 417NEL

shaft. A small coil near the drive shaft is connected to a microprocessor, which detectssmall variations in electric current. As both magnets rotate past the coil, they induce asmall, brief pulse of electric current, registered by the microprocessor. The frequencyof the pulses indicates the speed of rotation of the shaft and, therefore, the speed of thevehicle. If the driver sets the cruise control at a certain speed, the microprocessor can main-tain that speed by sending a signal to a control mechanism which injects more fuel intothe engine if the frequency decreases, less if the frequency increases.

Currents can be produced in a loop of wire rotated in a uniform magnetic field and con-nected to a galvanometer in its ammeter configuration (Figure 6). The magnetic fieldthrough the loop is changing most when the loop is perpendicular to the field (raising thecurrent to its maximum) and is not changing when it is parallel (the current drops tozero for an instant). This principle is fundamental to the construction of generators.

What determines the direction of the induced current? In 1834, Heinrich Lenz, usingthe law of conservation of energy, discovered the answer. Lenz reasoned that when thefield from a moving bar magnet induces a current in a solenoid, this current gives riseto another magnetic field (the “induced” field). There are only two possible directionsfor the flow of charge through the coil. Let us assume that the current spirals towardthe magnet when a N-pole is pushed into the coil, as in Figure 7. The right-hand rule forcoils then tells us that the right end of the coil becomes a S-pole, attracting the magnet.

Lenz reasoned that this situation is not possible because the attractive force will speedup the magnet, increasing its kinetic energy, inducing a larger current (more energy)and increasing the induced magnetic field (with the magnet speeded up still further,making its kinetic energy even higher). Since the total energy of the system cannotincrease, our assumption must be false, and the current in the solenoid must spiral awayfrom the incoming N-pole, as in Figure 8.

Therefore, the near end of the coil is a N-pole. The moving bar magnet induces a cur-rent in the coil which produces a magnetic field in opposition to the inward motion ofthe bar magnet. The work done in pushing the magnet into the coil against the opposinginduced field is transformed into electrical energy in the coil. Lenz summarized thisreasoning in Lenz’s law.

Section 8.5

SN

magnetplungedinto coil

Induced currentmakes near endof coil an S-pole.

SN

Figure 7Violating the law of conservation ofenergy

B

Figure 6A current is produced in a coilrotating in a uniform magnetic field.

SN

magnetplungedinto coil

NS

Induced currentmakes near endof coil an N-pole.

Figure 8Obeying the law of conservation ofenergy

Lenz’s LawWhen a current is induced in a coil by a changing magneticfield, the electric current is in such a direction that its ownmagnetic field opposes the change that produced it.

418 Chapter 8 NEL

Keep in mind that Lenz’s law is consistent with the conservation of energy because theenergy lost by the magnet due to the induced field is equal to the energy gained by thecurrent due to the inducing field. The total energy remains constant.

Applying Lenz’s LawWe have already introduced the idea of a maglev train. But having studied the ideas ofLenz, we can examine another form of maglev train that uses Lenz’s law to levitate thetrain above the rails. Powerful superconducting electromagnets at the bottom of thetrain pass above two rows of coils on the guideway. A current is induced in these coils.By Lenz’s law, the current acts to oppose the downward motion of the electromagnets,keeping the train hovering safely above the guideway (Figure 9).

Coils are not necessary for demonstrating Lenz’s law. If a magnetic field changes neara conducting plate, currents are induced within the plate, forming closed circular paths.These so-called eddy currents produce magnetic fields in opposition to the inducingaction. This principle is used in induction stoves. The surface of an induction stove isalways cool to the touch. If two pots—one glass, the other metal—are filled with waterand placed on such a stove, the water in the metal pot will boil, while the water in the glasspot will not heat up at all (Figure 10).

Below the surface of the stove are electromagnets operating on an AC current. Becausethe current is alternating, the magnetic field produced is not constant, inducing eddy cur-rents in the metal pot because metal acts as a conductor. No eddy currents are producedin the glass pot because glass acts as an insulator. The metal pot has some internal resist-ance, causing it to heat up. This heat is transferred to the water, causing it to boil.

PracticeUnderstanding Concepts

1. Explain how Faraday’s law of electromagnetic induction is applied in the operation ofa cruise-control device.

2. Explain how Lenz used the law of conservation of energy to determine the directionof the induced current produced by a moving magnet near a coil.

3. Two magnets are dropped through thin metal rings (Figure 11). One of the rings hasa small gap.(a) Will both magnets experience a retarding force? Explain your reasoning,

sketching the magnetic fields of the falling magnets and any induced currents orcurrent-created magnetic fields.

(b) Will your answers change if the rings are replaced with long cylinders, one with along thin gap down one side?

N

S S

N

Figure 11For question 3

superconductingmagnet

cryogeniccompressor

landingwheel

guidewaylevitation

coil

propulsioncoil

Figure 9Superconducting electromagnetsinduce currents in coils beneath themaglev train. By Lenz’s law, thesecurrents set up magnetic fieldsopposing the downward motion ofthe train, thus lifting it above therails.

metal pot

glass pot

Figure 10The surface of an induction stove isalways cool to the touch. Water in ametal pot will boil; water in a glasspot will not heat up at all. Whywould it be unsafe to touch the topof an induction stove if you arewearing a metal ring?

Magnetic Fields and Electromagnetism 419NEL

Section 8.5

• The law of electromagnetic induction states that an electric current is induced ina conductor whenever the magnetic field in the region of the conductor changes.

• The greater the change in the magnetic field per unit time, the larger the inducedcurrent.

• Lenz’s law states that when a changing magnetic field induces a current in a con-ductor, the electric current is in such a direction that its own magnetic fieldopposes the change that produced it.

Electromagnetic InductionSUMMARY

Section 8.5 QuestionsUnderstanding Concepts

1. Examine the circuit shown in Figure 12. When the switchis closed, assume the magnetic field produced by the sole-noid is very strong.(a) Explain what will happen to the copper ring (which is

free to move) when the switch is closed.(b) Explain what will happen to the copper ring when

there is a steady current in the circuit.(c) Explain what will happen to the copper ring when the

switch is opened.(d) How would your answers change if the terminals on

the power supply are reversed? Explain your answer.

2. Figure 13 shows a light bulb connected to a coil around ametal core. What causes the light bulb to glow?

3. A bolt of lightning can cause a current in an electric appli-ance even when the lightning does not strike the device.Explain how this could occur.

4. You place a copper ring onto an insulating stand inside asolenoid connected to an AC current. Explain what willhappen to the ring.

Applying Inquiry Skills

5. A coil of wire connected to a galvanometer is placed withits axis perpendicular to a uniform magnetic field. When thecoil is compressed, the galvanometer registers a current.Design an experiment to determine the factors that affectthe magnitude of the induced current in the coil.

6. Explain how you would construct a device for investigatingthe magnitude of the induced current produced by a movingbar magnet. Assume you have access to a bar magnet, acompass, a coil, and wire. You may not use a galvanometer.Draw a diagram of your device and explain how it works.

Making Connections

7. Explain how Lenz’s law is applied in levitating one type ofmaglev train.

8. Explain how an induction stove works.

9. Figure 14 shows a ground-fault interrupter, inserted forsafety between the power outlet and an appliance such asa clothes dryer. The ground-fault interrupter consists of aniron ring, a sensing coil, and a circuit breaker. The circuitbreaker interrupts the circuit only if a current appears in thesensing coil.(a) The circuit breaker will not interrupt the circuit if the

dryer is operating normally. Explain why.(b) If a wire inside the dryer touches the metal case,

charge will pass through a person touching the dryerinstead of going back through the ground-fault inter-rupter. How does the interrupter protect the person?

(c) Should all electrical devices be plugged into ground-fault interrupters? If so, why? If not, why not?

coil

iron coreswitch

battery

� �

copper ring(free to move)

Figure 12

Figure 13For question 4

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10. You are a civil engineer, seeking to reduce the number oftraffic jams along a very busy road during rush hour. Younotice that the side streets off the busy road often havegreen lights, causing the lights on the main road to be red,even in the absence of side-street traffic. You decide tosolve this problem by installing large coils of wire justbeneath the surface of the road, near the intersections onthe side streets. You connect the coils to small micro-processors in the traffic lights. Explain how your deviceworks and how it will help prevent traffic jams.

11. An amusement-park ride like the one in Figure 15 ele-vates riders on a lift, then drops them. The lift and theriders accelerate downward under the force of gravity.Research the method used to slow them down safely, andwrite a short report explaining the physics involved.Design another ride that uses the same principles.

12. Figure 16 is a schematic of an electric-guitar pickup, adevice that changes the vibrational energy of a guitarstring into sound.(a) Describe how the pickup works, explaining the need

for the string to vibrate and the purpose of the coiland permanent magnet.

(b) The string of the guitar vibrates in a standing-wavepattern, with a series of nodes and antinodes. Whereshould a pickup be placed to send the largest possiblecurrent to the amplifier?

heaterelement

ground-fault

interrupter

AC generator

iron ring

sensingcoil

circuit breaker

magneticfieldlines

Figure 14Schematic of a ground-fault interrupter (for question 9)

GO www.science.nelson.com

Figure 15For question 11

N S

N

S

to amplifier

iron core

guitar string(magnetizable)

side view

coil

Figure 16The schematic of a pickup on an electric guitar(for question 12)