Chapter 21Magnetic Induction

Magnetic InductionElectric and magnetic forces both act only on

particles carrying an electric chargeMoving electric charges create a magnetic fieldA changing magnetic field created an electric field

This effect is called magnetic inductionThis links electricity and magnetism in a fundamental

wayMagnetic induction is also the key to many practical

applications

ElectromagnetismElectric and magnetic phenomena were connected

by Ørsted in 1820He discovered an electric current in a wire can exert a

force on a compass needleIndicated a electric field can lead to a force on a

magnetHe concluded an electric field can produce a magnetic

fieldDid a magnetic field produce an electric field?

Experiments were done by Michael Faraday

Section 21.1

Faraday’s ExperimentFaraday attempted to

observe an induced electric fieldHe didn’t use a lightbulb

If the bar magnet was in motion, a current was observed

If the magnet is stationary, the current and the electric field are both zero

Section 21.1

Another Faraday Experiment

A solenoid is positioned near a loop of wire with the lightbulbHe passed a current through the solenoid by connecting it to a

batteryWhen the current through the solenoid is constant, there is no

current in the wireWhen the switch is opened or closed, the bulb does light up

Section 21.1

Conclusions from ExperimentsAn electric current is produced during those

instances when the current through the solenoid is changing

Faraday’s experiments show that an electric current is produced in the wire loop only when the magnetic field at the loop is changing

A changing magnetic field produces an electric fieldAn electric field produced in this way is called an

induced electric fieldThe phenomena is called electromagnetic induction

Section 21.1

Magnetic FluxFaraday developed a quantitative theory of induction

now called Faraday’s LawThe law shows how to calculate the induced electric

field in different situationsFaraday’s Law uses the concept of magnetic flux

Magnetic flux is similar to the concept of electric fluxLet A be an area of a surface with a magnetic field

passing through itThe flux is ΦB = B A cos θ

Section 21.2

Magnetic Flux, cont.

If the field is perpendicular to the surface, ΦB = B A

If the field makes an angle θ with the normal to the surface, ΦB = B A cos θ

If the field is parallel to the surface, ΦB = 0

Section 21.2

Magnetic Flux, finalThe magnetic flux can be defined for any surface

A complicated surface can be broken into small regions and the definition of flux applied

The total flux is the sum of the fluxes through all the individual pieces of the surface

The unit of magnetic flux is the Weber (Wb)1 Wb = 1 T . m2

Section 21.2

Faraday’s LawFaraday’s Law indicates how to calculate the

potential difference that produces the induced currentWritten in terms of the electromotive force induced in

the wire loop

The magnitude of the induced emf equals the rate of change of the magnetic flux

The negative sign is Lenz’s Law

Bεt

Section 21.2

Applying Faraday’s LawThe ε is the induced

emf in the wire loopIts value will be

indicated on the voltmeter

It is related to the electric field directly along and inside the wire loop

The induced potential difference produces the current

Applying Faraday’s Law, cont.The emf is produced by changes in the magnetic

flux through the circuitA constant flux does not produce an induced voltage

The flux can change due toChanges in the magnetic fieldChanges in the areaChanges in the angle

The voltmeter will indicate the direction of the induced emf and induced current and electric field

Section 21.2

Faraday’s Law, SummaryOnly changes in the magnetic flux matterRapid changes in the flux produce larger values of emf

than do slow changesThis dependency on frequency means the induced emf

plays an important role in AC circuitsThe magnitude of the emf is proportional to the rate of

change of the fluxIf the rate is constant, then the emf is constantIn most cases, this isn’t possible and AC currents result

The induced emf is present even if there is no current in the path enclosing an area of changing magnetic flux

Section 21.2

Flux Though a Changing AreaA magnetic field is

constant and in a direction perpendicular to the plane of the rails and the bar

Assume the bar moves at a constant speed

The magnitude of the induced emf is ε = B L v

The current leads to power dissipation in the circuit

Section 21.2

Conservation of EnergyThe mechanical power put into the bar by the

external agent is equal to the electrical power delivered to the resistor

Energy is converted from mechanical to electrical, but the total energy remains the same

Conservation of energy is obeyed by electromagnetic phenomena

Section 21.2

Electrical GeneratorNeed to make the rate

of change of the flux large enough to give a useful emf

Use rotational motion instead of linear motion

A permanent magnet produces a constant magnetic field in the region between its poles

Section 21.2

Generator, cont.A wire loop is located in the region of the fieldThe loop has a fixed area, but is mounted on a

rotating shaftThe angle between the field and the plane of the

loop changes as the loop rotatesIf the shaft rotates with a constant angular velocity,

the flux varies sinusoidally with timeThis basic design could generate about 70 V so it is

a practical design

Section 21.2

Changing a Magnetic Flux, SummaryA change in magnetic flux and therefore an induced

current can be produced in four waysIf the magnitude of the magnetic field changes with

timeIf the area changes with timeIf the loop rotates so that the angle changes with timeIf the loop moves from one region to another and the

magnitude of the field is different in the two regions

Section 21.2

Lenz’s LawLenz’s Law gives an

easy way to determine the sign of the induced emf

Lenz’s Law states the magnetic field produced by an induced current always opposes any changes in the magnetic flux

Section 21.3

Lenz’s Law, Example 1

Assume a metal loop in which the magnetic field passes upward through it

Assume the magnetic flux increases with timeThe magnetic field produced by the induced emf must oppose the

change in fluxTherefore, the induced magnetic field must be downward and the

induced current will be clockwise

Section 21.3

Lenz’s Law, Example 2

Assume a metal loop in which the magnetic field passes upward through it

Assume the magnetic flux decreases with timeThe magnetic field produced by the induced emf must oppose the

change in fluxTherefore, the induced magnetic field must be downward and the

induced current will be counterclockwise

Section 21.3

Problem Solving StrategyRecognize the principle

The induced emf always opposes changes in flux through the Lenz’s Law loop or path

Sketch the problemShow the closed path that runs along the perimeter of

a surface crossed by the magnetic field linesIdentify

Is the magnetic flux increasing or decreasing with time?

Section 21.3

Problem Solving Strategy, cont.Solve

Treat the perimeter of the surface as a wire loopSuppose there is a current in the loopDetermine the direction of the resulting magnetic fieldFind the current direction for which this induced magnetic

field opposes the change in the magnetic fluxThis current direction gives the sign (direction) of the

induced emfCheck

Consider what your answer meansCheck that your answer makes sense

Section 21.3

Lenz’s Law and Conservation of EnergyMathematically, Lenz’s Law is just the negative sign

in Faraday’s LawIt is actually a consequence of conservation of

energyTherefore, conservation of energy is contained in

Faraday’s LawNowhere in the laws of electricity and magnetism is

there any explicit mention of energy or conservation of energy

Physicists believe all laws of physics must satisfy the principle of conservation of energy

Section 21.3