Given:

Radius of circular coil

Magnetic field intensity

Angular speed of coil ω =

Magnetic flux through the circular coil ϕ can be given by formula

…(i)

As

Where ω =angular velocity of loop

Where θ is the angle between magnetic field and area vector of loop.

by faraday’s law of electromagnetic induction

Where

ϵ =emf produced

ϕ =flux of magnetic field

putting the value of eqn.(i) in above eqn. we get,

…(ii)

Since maximum value of is equal to 1

Putting the values of B, A and ω we get,

………. (iii)

Therefore maximum emf induced in the circular coil is

(b) from eqn.(ii) emf induced in the coil is given by

Average value of induced emf is given by formula

Where is the time taken by the coil to complete one revolution

Therefore, average induced emf is zero

(c). the average of squares of induced emf is given by the formula

Putting the values of B, A and ω we get

using eqn.(iii)

Therefore average of squares of emf produced is