Question

A circular coil of n turns and radius r is kept normal to magnetic fieldby b=bcoswt deduce an expression for the emf induced in this coil

Answer 1

Area of the coil, A = πr2

Magnetic field of the coil, B = Bocosωt

=> Magnetic flux linked with the coil, Φ = NB.A

=>  Φ = NBA cos0

=>  Φ = NBA 

Induced emf, e = - dΦ/dt = ωNABosinωt

Answer 2

The expression of the coil is ωNABosinωt.

Radius of the coil = r (Given)

Magnetic field of the coil = b = bcosωt (Given)

Area of the coil = A = πr²

Magnetic field of the coil = B = Bocosωt

Magnetic flux linked with the coil, Φ = nb.A

Φ = nbA cos0

Φ = nbA  

Therefore, the Induced emf will be -

e = - dΦ/dt

= ωNABosinωt

Therefore, the expression of the coil is ωNABosinωt.