Electromagnetic Induction Law
Following are the two laws of electromagnetic induction as given by faraday. Both the laws follow from faraday's experiments discussed above.
First law: Whenever the amount of magnetic flux linked with a circuit changes and is induced in the circuit. The induced lasts so long as the change in magnetic flux continues.
Second law: the magnitude of induced in a circuit is directly proportional to the rate of change of magnetic flux linked with the circuit.
Explanation
First law. In faraday experiment when magnet is moved towards a coil number of magnetic lines of force lined with the coil increase magnetic flux increase. When the magnet is moved away, the magnetic flux linked with the coil decreases. In both the cases, galvanometer shows deflection indicating that is induced in the coil.
When there is no relative motion between the magnet and the coil, magnetic flux linked with the coil remains constant. That is why galvanometer shows no deflection. Thus induced is produced when magnetic flux changes and induced continues so long as the change in magnetic flux continues. This is first law. The same results follow from faraday's second experiment.
Second law: In faraday's experiment when magnet is moved faster the magnetic flux linked with the coil changes at a faster rate. Therefore galvanometer deflection is more. However when the magnet is moved slowly rate of change of magnetic flux is smaller. Therefore galvanometer deflection is smaller induced is smaller. Hence magnitude of induced varies directly as the rate of change of magnetic flux linked with the coil. This is second law.
If ∅1 is amount of magnetic flux linked with a coil at any time and ∅2 is the magnetic flux linked with the coil after t sec, then
Rate of change of magnetic flux = ∅2 - ∅1 / t
According to faraday's second law induced
E ∝ (∅2 - ∅1 ) / t or e = K (∅2 - ∅1) / t
Where k is a constant of proportionality.
As k = 1 (in all systems of units)
∴ E = ∅2 - ∅1 / t
If d ∅ is small change in magnetic flux in a small time dt we can rewrite
E = - d ∅ / dt
Negative sign is taken because induced always opposes any change in magnetic flux associated with the circuit. This follows from Lenz's law discussed in art
In case of a closely wound coil of N turns change in magnetic flux associated with each turn is the same. Therefore total induced is given by e - - N d∅ / dt
By increasing number of turns N in the coil we can increase the induced
The magnetic flux threading a coil changes from 12 x 10 Wb to 6 x 10 Wb in 0 . 01 calculate the induced
Sol here, ∅1 = 12 x 10-3 Wb,
∅ 2 = 6 x 10 -3 Wb
Dt = 0.01s = 10-2s e =?
E = - d∅ / dt = - (∅2 - ∅1)
= - (6 x 10 - 12 x 10) / 10-2 = 0.6 volt.
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