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Chapter 27, 28 & 29: Magnetism &

Electromagnetic Induction

•Magnetic flux

•Faraday’s and Lenz’s law

•Electromagnetic Induction

•Ampere’s law

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Magnetic Flux and Faraday’s Law of Electromagnetic

Induction

• Induced Electromotive

Force

• Magnetic Flux

• Faraday’s Law of Induction

• Lenz’s Law

• Mechanical Work and

Electrical Energy

We have seen that current carrying wire generates a magnetic field

around itself. Lets look at the other side of the coin,

Can a magnetic field generate an electric current?

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Induced Electromotive Force: Faraday’s Experiments

• Michael Faraday (1831) found that when a bar magnet was moved towards a coil of wire that was connected to a sensitive galvanometer, the galvanometer gave a momentary deflection showing that an electric current had been induced.

• When the magnet was moved away from the galvanometer, the galvanometer deflected in opposite direction.

• No current was induced when the magnet was held stationary inside or outside the coil.

• The process of setting up a current in the coil of wire through the relative motion of magnet and the coil is called Electromagnetic Induction.

• Faraday found that the induced current and the emf depends on

(i) the number of turns in the coil,

(ii) the strength of the magnet

(iii) the speed with which the magnet is moved towards or away from the coil

(iv) the core of the coil, e.g. an iron core induces more current

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Induced Electromotive Force

Note the motion of the magnet in each image:

Away

Stationary

Towards

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Induced Electromotive Force

Faraday’s experiment: closing the switch in the primary

circuit induces a current in the secondary circuit, but

only while the current in the primary circuit is changing.

Iron Bar

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Induced Electromotive Force

• The current in the secondary circuit is zero as long as

the current in the primary circuit, and therefore the

magnetic field in the iron bar, is not changing.

• Current flows in the secondary circuit while the current

in the primary is changing. It flows in opposite directions

depending on whether the magnetic field is increasing or

decreasing.

• The magnitude of the induced current is proportional to

the rate at which the magnetic field is changing.

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Magnetic Flux

Magnetic Flux (): The flux (d) of magnetic field passing through a small

area dA is defined as the product of the area and the NORMAL

component of B through the area.

Flux is a scalar quantity. The total flux through a larger area is simply

the integral of small elemental components

A B

BA

A

B

cosB

cosBA

B

A

dAB

dABd

A: is the surface

area vector

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Magnetic Flux

Magnetic flux is used in the

calculation of the induced emf.

If the area is of some complicated

shape and B is not uniform, the

magnetic flux can be written as the

integral of elemental components.

dAB

dABd

Magnetic Flux is a measure of the number of

magnetic field lines that cross a given area.

BA

0

Where is the angle between the normal

to the area (loop) and magnetic field

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Faraday’s Law of Induction

From a consideration of experiments involving the production of an

induced emf in a coil by either a changing magnetic field or a changing

current, Faraday developed the following law.

Faraday’s law: The emf induced in a circuit is equal to the rate of

change of magnetic flux through the circuit. OR When ever the

magnetic flux linked with any circuit changes an emf () is induced. i.e.

The induced emf is proportional to the rate of change of magnetic flux

and to the number of turns (N) in the circuit.

Minus sign reminds us

of the direction in which

the induced emf or

induced current acts -

Lenz’s law

Faraday’s Law of Induction

There are many devices that operate on the basis of

Faraday’s law of Electromagnetic Induction.

An electric guitar

pickup:

Tape recorder:

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Lenz’s Law

Lenz’s Law:

An induced current always flows in a direction that

opposes the change that produced it. i.e. An induced emf

gives rise to an induced current which sets up a magnetic

field to oppose the original change in flux.

Therefore, if the magnetic field is increasing, the magnetic field

created by the induced current will be in the opposite direction; if

decreasing, it will be in the same direction.

v v

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Magnetic field of Induced Current – LENZ LAW

Consider the case: N-pole of a bar magnet being moved towards a coil

Magnetic field

of magnet

Magnetic field

of magnet

As the N-pole moves closer to

the coil, more field lines pass

through the coil, the magnetic

flux changes and hence emf is

induced.

The induced current sets up a

magnetic field to oppose the

change in flux. It sets up a N-

pole on the left side of the coil

to repel the N-pole of the bar

magnet, thus the field lines are

opposite to that of bar magnet

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Magnetic Flux and Induced emf

Exercise: A 0.055 T magnetic field passes through a

circular ring of radius 3.1 cm at an angle of 16° with

the normal. Find the magnitude of the magnetic flux

through the ring.

Exercise: A 0.25 T magnetic field is perpendicular to a

circular loop of wire with 53 turns and a radius of 15

cm. If the magnetic field is reduced to zero in 0.12 s,

what is the magnitude of the induced emf?

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EMF Induced in a Moving Conductor

Consider a conducting metal rod of length l sliding with speed v (towards

right) over two horizontal wires placed in a magnetic field B.

This conducting rod completes the circuit. As it slides, the magnetic

flux increases, and a current is induced and the bulb lights up.

The induced current sets up a magnetic force in the opposite direction

to oppose the motion of the rod.

This diagram shows the variables we need to calculate the induced

emf.

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Induced emf:

Thus induced emf depends on the strength of the magnetic field and

the speed and length of the conducting rod

If the rod is to move at a constant speed, v, an external

force must be exerted on it. This force should have equal

magnitude and opposite direction to the magnetic force:

If the rod moves with a speed v, it travels a distance, dx = vdt, in

time dt, thus the change in the area of loop, dA = ldx = lvdt

Blv

dt

lvdtB

dt

dAB

dt

d

EMF Induced in a Moving Conductor

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Mechanical Work and Electrical Energy

The mechanical power delivered by the external force

is:

Compare this to the electrical power in the light bulb:

Therefore, mechanical power has been converted directly

into electrical power.

This simple example of motional emf illustrates the basic

principle behind the generation of virtually all the world’s

electrical energy.

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EMF Induced in a Moving Conductor

Questions: In the following set of experiments, a galvanometer is

used to detect a current flow. Mark in the direction of the current or

write zero if appropriate

x x x x x

x x x x x

x x x x x

x x x x x

v

x x x x x

x x x x x

x x x x x

x x x x x

v

x x x x x x

x x x x x x

x x x x x x

x x x x x x

v

x x x x x

x x x x x

x x x x x

x x x x x

v

(i) Loop moving into

a uniform field

(ii Loop moving through

a uniform field

(iii) Loop moving out

of a uniform field

(iv) Field moving while

loop is stationary

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EMF Induced in a Moving Conductor

x x x x x

x x x x x

x x x x x

x x x x x

x x x

x x x

x x x

x x x x x

x x x x x

x x x x x

x x x x x

(v) Loop and field both stationary

(vi) Magnitude of field increasing with time, Loop stationary

Initial Final

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EMF Induced in a Moving Conductor

Question: Consider a rectangular conducting loop of dimensions

4 cm 2 cm moving at a constant speed of 2 cm/s through a

uniform magnetic field of strength 0.5 T as shown. Sketch the

variation of magnetic flux through the coil and the induced emf.

4 cm

8 cm

2 cm

2 cm/s

Answer: In this question students must realise that as long as the

loop is outside the field, there is no change in magnetic flux, thus

emf is zero. When the loop starts to enter the field, magnetic flux

changes. It changes for 2 s, as it requires 2 s for the loop to

completely enter the magnetic field. Once the entire loop is in the

field, there is no change in flux (Max flux) for the next 2 s, as it takes

2s for the leading edge of the loop to reach the end of the field. Once

the loop starts to leave the field, the flux changes for the next 2 s

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(Wb)

t (s) 0 6 4 2

4 10-4

8 cm

4 cm

2 cm

2 cm/s

t (s)

emf

(V) 2 10-4

-2 10-4

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EMF Induced in a Moving Conductor

5 cm 5 cm

2 cm

2 cm/s

5 cm 5 cm

Question: Repeat the previous problem with the following loop

dimensions and field configurations: L = 5 cm, W = 2 cm, B =2T,

v = 2 cm s-1 and R =0.2