A circular loop of radius a having `n` turns is kept in a horizontal plane. A uniform magnetic field `B` exists in a vertical direction as shown in Fig.313. Find the emf induced in the loop if the loop is roated with a uniform angualr velocity `omega` about
(a) an axis passing through the center and perendicular to the plane of the loop.
(b) the diameter.

Explanation

(a) The emf induced when there is change of flux. As in this case (Fig 3.13), there is no change of flux, hence no emf will be induced in the coil.
(b) If the loop is rotated about the diameter there will be of flux with time. In this case, emf, will be induced in the coil. The area of the loop id `A = pia^(2)`. If the normal of the loop makes an angle `theta = 0` with the magnetic field at `t = 0`, this angle will become `theta = omegat` at time `t`. The flux of the magnetic field at this time is

`phi = nBpia^(2) cos theta = nBpia^(2) cos omegat`
The induced emf is `epsilon` is coming out to be positive, so the direction of induced emf will be as shown in Fig.3.14. Because here this sence is positive if we look at the direction of area vector.