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.