Michael Faraday a British scientist stated two laws of electromagnetic induction.
At any time the number of magnetic lines of force linking with a coil / or circuit changes, an e.m.f gets induced in that coil or circuit.
The magnitude of the induced e.m.f is directly proportional to the rate of change of flux linkages.
∴ Flux linkages = Flux x Number of turns of coil
The law can be explained as below:
- Think through a coil having N turns.
- The initial flux linking with a coil is ф1.
- Initial flux linkages = Nф1.
In time interval t, the flux linking with the coil changes from ф1 to ф2.
∴ Final flux linkages = Nф2 and,
Rate of change of flux linkages = (Nф2 - Nф1) / t
Now as per the first law, e.m.f will get induced in the coil and as per second law the magnitude of e.m.f. is proportional to the rate of change of flux linkages.
∴ e ∝ (Nф2 - Nф1) / t
e = K.(Nф2 - Nф1) / t
e = N.(dф/dt)
With K as unity to get units of e as volts, dф is change in flux, dt is change in time hence (dф / dt) is rate of change of flux.
Now as per Lenz's law, the induced e.m.f. sets up a current in such a direction so as to oppose the very cause producing it. Mathematically this opposition is expressed by a negative sign.
Thus such an induced e.m.f. is mathematically expressed along with its sign as,
∴ E = -N(dф/dt) volts