Chapter 23

Faraday’s Law

and

Induction

2

23.1 Michael Faraday 1791 – 1867 British experimental

physicist Contributions to early

electricity include Invention of motor,

generator, and transformer

Electromagnetic induction

Laws of electrolysis

3

Induction A changing magnetic field produces an

induced current on a circuit without the present of a battery in the circuit

There is an induced emf associated with the induced current

Faraday’s Law of Induction describes the induced emf

4

EMF Produced by a Changing Magnetic Field,

When the magnet is held stationary, there is no deflection of the ammeter

Therefore, there is no induced current Even though the magnet is inside the loop

5

EMF Produced by a Changing Magnetic Field,

A loop of wire is connected to a sensitive ammeter When a magnet is moved toward the loop, the

ammeter deflects The deflection indicates a current induced in the wire

6

EMF Produced by a Changing Magnetic Field,

The magnet is moved away from the loop The ammeter deflects in the opposite

direction

7

EMF Produced by a Changing Magnetic Field, Summary The ammeter deflects when the magnet is

moving toward or away from the loop The ammeter also deflects when the loop is

moved toward or away from the magnet An electric current is set up in the coil as long

as relative motion occurs between the magnet and the coil This is the induced current that is produced by an

induced emf

8

Faraday’s Experiment – Set Up

A primary coil is connected to a switch and a battery

The wire is wrapped around an iron ring

A secondary coil is also wrapped around the iron ring

There is no battery present in the secondary coil

The secondary coil is not electrically connected to the primary coil

9

Faraday’s Experiment – Findings

At the instant the switch is closed, the galvanometer (ammeter) needle deflects in one direction and then returns to zero

When the switch is opened, the galvanometer needle deflects in the opposite direction and then returns to zero

The galvanometer reads zero when there is a steady current or when there is no current in the primary circuit

10

Faraday’s Experiment – Conclusions

An electric current can be produced by a time-varying magnetic field This would be the current in the secondary circuit of this

experimental set-up The induced current exists only for a short time

while the magnetic field is changing This is generally expressed as: an induced emf is

produced in the secondary circuit by the changing magnetic field The actual existence of the magnetic field is not sufficient

to produce the induced emf, the field must be changing

11

Magnetic Flux To express

Faraday’s finding mathematically, the magnetic flux is used

The flux depends on the magnetic field and the area:

B d B A

12

Faraday’s Law – Statements Faraday’s Law of Induction states that

the emf induced in a circuit is equal to the time rate of change of the magnetic flux through the circuit

Mathematically,

Bd

dt

13

Faraday’s Law – Example Assume a loop

enclosing an area A lies in a uniform magnetic field

The magnetic flux through the loop is B = B A cos

The induced emf is cos

dBA

dt

14

Ways of Inducing an emf The magnitude of the field can change

with time The area enclosed by the loop can

change with time The angle between the field and the

normal to the loop can change with time Any combination of the above can occur

15

Applications of Faraday’s Law – Pickup Coil

The pickup coil of an electric guitar uses Faraday’s Law

The coil is placed near the vibrating string and causes a portion of the string to become magnetized

When the string vibrates at the some frequency, the magnetized segment produces a changing flux through the coil

The induced emf is fed to an amplifier

16

17

18

19

20

23.2 Motional emf A motional emf is one

induced in a conductor moving through a magnetic field

The electrons in the conductor experience a force that is directed along l

B q F v B

21

Motional emf, cont Under the influence of the force, the electrons

move to the lower end of the conductor and accumulate there

As a result of the charge separation, an electric field is produced inside the conductor and gives rise to an electric force on the electrons

The charges accumulate at both ends of the conductor until the electric and magnetic forces are balanced

22

Motional emf, final For balance, q E = q v B or E = v B A potential difference V=vBl between the

two ends of the conductor is maintained as long as the conductor continues to move through the uniform magnetic field

If the direction of the motion is reversed, the polarity of the potential difference is also reversed

23

Sliding Conducting Bar

A bar moving through a uniform field and the equivalent circuit diagram

Assume the bar has zero resistance The work done by the applied force appears as

internal energy in the resistor R

24

Sliding Conducting Bar, cont The induced emf is

Since the resistance in the circuit is R, the current is

Bd dxB B v

dt dt

B vI

R R

25

Sliding Conducting Bar, Energy Considerations The applied force does work on the

conducting bar This moves the charges through a magnetic

field The change in energy of the system during

some time interval must be equal to the transfer of energy into the system by work

The power input is equal to the rate at which energy is delivered to the resistor

2

appF v I B vR

26

27

28

29

30

31

32

33

34

35

36

AC Generators Electric generators take

in energy by work and transfer it out by electrical transmission

The AC generator consists of a loop of wire rotated by some external means in a magnetic field

37

Induced emf In an AC Generator

The induced emf in the loops is

This is sinusoidal, with max = N A B

sin

BdN

dtNAB t

38

23.3 Lenz’ Law Faraday’s Law indicates the induced

emf and the change in flux have opposite algebraic signs

This has a physical interpretation that has come to be known as Lenz’ Law

It was developed by a German physicist, Heinrich Lenz

39

Lenz’ Law, cont Lenz’ Law states the polarity of the

induced emf in a loop is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop

The induced current tends to keep the original magnetic flux through the circuit from changing

40

Lenz’ Law – Example 1

When the magnet is moved toward the stationary loop, a current is induced as shown in a

This induced current produces its own magnetic field that is directed as shown in b to counteract the increasing external flux

41

Lenz’ Law – Example 2

When the magnet is moved away the stationary loop, a current is induced as shown in c

This induced current produces its own magnetic field that is directed as shown in d to counteract the decreasing external flux

42

43

44