Explain how Emf Induced by Changing the Area Enclosed by the Coil

Emf induced by changing the area enclosed by the coil

Let consider, PQRS is a conductor bent in the shape as shown in the Figure. L1M1 is a sliding conductor of length l resting on the arms PQ and RS.


Fig: Emf induced by changing the area

A uniform magnetic field ‘B’ acts perpendicular to the plane of the conductor. The closed area of the conductor is L1QRM1. When L1M1 is moved through a distance dx in time dt, the new area is L2QRM2. Due to the change in area L2L1M1M2, there is a change in the flux linked with the conductor. Therefore, an induced emf is produced.

Change in area dA = Area L2L1M1M2

∴ dA = l dx

Change in the magnetic flux, dφ = B.dA = Bl dx

But e = – dφ/dt

∴ e = – Bl dx/dt = – Bl v

where v is the velocity with which the sliding conductor is moved.

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