A ring rotates with angular velocity `omega` about an axis in the plane of the ring which passes through the center of the ring. A constant magnetic field `B` exists perpendicualr to the plane of the ring . Find the emf induced in the ring as a function of time.

Explanation

At any time `t phi =BA cos theta =BA cos omegat`
Now induced `emf` in the loop
`e=(-dphi)/(dt)=BA omegasin omegat`
If there are `N` turns
`emf=BA omega N sin omegat`
`BaomegaN` is the amplitude to the `emf`
`e=e_(m)sin omegat`
`i=e/R=(e_(m))/R sin wt=i_(m) sin wt`
`i_(m)=e_(m)/R`
The rotating coil thus produces a sinusoidally varying current or alternating current.This is also the principle used in generator.