FARADAY'S LAWOF

INDUCTION

SLIDES PREPARED BY ZIL E HUMA

OBJECTIVES.• FARADAY’S EXPERIMENTS.

• FARADAY’S LAW OF ELECTROMEGNATIC INDUCTION

• LENZ’ LAW

• MOTIONAL EMF

FARADAY’S EXPERIMENTS:

Experiment No. 1

N

S

A

v

Figures shows a coil of wire as a part of a circuit containing an Ammeter.

Normally we would expect the Ammeter to show no current in the circuit because they seems to be no electro-motive force.

However, if we push a bar magnet towards a coil with its north pole facing the coil, the ammeter deflects, showing that a current has been setup in the coil.

If we move the magnet away from the coil, the meter again deflects, but in the opposite direction, which means that the current in the coil is in the opposite direction.

If we use the south pole end of a magnet instead of the north pole ends, the experiment works as described above but the deflection is reversed.

The faster the magnet is moved, the greater is the reading of the meter.

Further experimentation shows that what matters is the relative motion of the magnet and the coil. It makes no difference whether we move the magnet towards the coil or the coil towards the magnet.

The current that appears in this experiment is called an induced current and is said to be set up by an induced electro-motive force.

A

The coils are placed close together but at rest with respect to each other.

S

Experiment No. 2

When we close the switch S, setting up the steady current in the right hand coil, the meter deflects momentarily.

When we open the switch thus interrupting this current, the meter again deflects momentarily but in the opposite direction.

o Experiments shows that there is an induced EMP in the left coil. Whenever, the current in the right coil is changing.

o It is the rate at which the current is changing and not the size of the current that is significance.

o The common features of these two experiments is motion or change.

o It is the moving magnet or the changing current that is responsible for the induced EMF.

FARADAY’S LAW OF INDUCTION. Imagine that there are lines of magnetic

field coming from the bar magnet of first figure and from the right hand current.

Some of those field lines pass through the left hand coil in both figures.

As the magnet is moved in the situation of Fig. 1 or as the switch is opened or closed in figure 2, the number of lines of the magnetic field passing through the left hand coil changes.

As Faraday’s experiments and technique of field lines helps us to visualize that, It is the change in the number of field lines passing through a circuit loop that induces the emf in the loop. Specifically, it is the rate of change in the number of field lines passing through the loop that determines the induced emf.

Like the electric flux the magnetic flux can be considered to be a measure of field lines passing through any surface is defined as

B = B*dA

MAGNETIC FLUX

Here dA is an element of area of the surfaceThe integration is carried out over the entire surface through which we wish to calculate the flux.

The surface enclose by the left hand loop, the magnetic field has a constant magnitude and direction over a planar area A, the flux can be written

B = BA cos

Where is the angle between the normal to the surface and the direction of the field.

The SI unit of magnetic flux is the tesla-meter2, which is given the name of weber (abbreviation Wb).

1 weber=1 tesla.meter2

SI UNIT OF MAGNETIC FIELD

The induced emf in a circuit is equal to the negative of the rate at which the magnetic flux through the circuit is changing with time.

In Mathematical terms faraday’s law is

= -dB /dt

Where is the induced emf.

If the coil consist of N turns then an induced emf appears in every turns and the total induced emp in the circuit is the sum of the individual values, just as in the case of batteries connected in series. So the total induced emf will be

= -NdB /dt.

Def:“The induced current in a close conducting loop appears in such a direction that it opposes that change that produced it”.

LENZ’ LAW

The –ve sign in the faraday’s law suggest this opposition.Consider the first faraday’s experiment, the north pole of the magnet and the cross section of a nearby conducting loop, as we push the magnet towards the loop or the loop towards the magnet, an induced current is setup in the loop.