## Saturday, September 10, 2016

### Self Induction and Mutual Induction

Basing on the experimental results, Faraday made some conclusions. Experimental arrangement can be shown below.

They are
1.   When a magnetic flux linked with a  closed circuit changes, an induced EMF and induced current is developed in that closed circuit.

2.   Induced EMF exists until there is a change in the magnetic flux.

3.   EMF developed in the closed circuit is directly proportional to the rate of change in the magnetic flux.

If the flux is due to the number of coils, there is EMF in each coil and the total EMF is the sum of all of them. We can write magnetic flux as the dot product of magnetic field induction and area of cross section. As they are in the same direction, the cos angle is equal to one and maximum. The total magnetic EMF can be written as shown in the figure.

We can defile self induction coefficient as shown below. It is simply the magnitude of the induced EMF in a closed circuit when the rate of change of flux is one unit.

To find the direction of the induced EMF, we can use a law called Fleming right hand thumb rule. According to this rule,

If a fore finger indicates the direction magnetic field, thumb indicates the direction of the conductor then the central finger indicates the direction of the induced current in the closed circuit.

We can also find out the charge and the induced current at a given circuit due to induction as shown in the diagram below.

Problem and solution

Magnetic flux is given in the problem and we need to find induced current in the closed circuit. We can do that by differentiating the flux with time so that we get induced EMF in the circuit. Further we can write that induced EMF as the ratio of induced current and resistance. By substituting the resistance value in the circuit, we can measure the current in the circuit as shown in the diagram below.

Mutual induction

This is the induced EMF generated in the secondary coil due to change in the magnetic flux in the first coil. The first coil is having a battery and a key to control the flow of current. The second coil consists of a galvanometer. When the switch in the first coil is just switched on or off, change in the reading of the galvanometer is noticed. Thus emf is developed in the second coil due to change in the flux in the first coil.

Basing on this concept, we can define the mutual inductance and its coefficient as shown in the diagram below.

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