A coil of area `A` lies in a uniform magnetic field `B` with its plane perpednicular to the field. In this position the normal to the coil makes an angle `0^(@)` with a field. The coil rotates at a uniform rate about its diameter to complete one rotation in time `T` . Find the average induced e.m.f. in the coil during the interval when coil rotates from:
(a) `0^(@)` to `90^(@)`
(b) `90^(@)` to `I80^(@)`
(c) `I80^(@)` to `270^(@)`
(d) `270^(@)` to `360^(@)`

Explanation

`phi_(I)=BA`
`phi=BAcos90^(@)=0`
`Deltat=(T)/(4)`
`|bar(e)|=(Deltaphi)/(Deltat)=(BA)/(T//4)=(4BA)/(T)`
(b) `phi_(I)=0` , `phi_(2)=BAcosI80^(@)=-BA` , `Delat t=(T)/(4)`
`|bar(e)|=(Deltaphi)/(Deltat)=(BA)/(T//4)=(4BA)/(T)`
(c) `phi_(I)=-BA` , `phi_(2)=BAcos270^(@)=0` ,. `Deltat=(T)/(4)`
`|bar(e)|=(Deltaphi)/(Deltat)=(BA)/(T//4)=(4BA)/(T)`
`phi_(I)=0` , `phi_(2)=BAcos360^(@)=BA , Deltat=(T)/(4)`
`|bar(e)|=(Deltaphi)/(Deltat)=(BA)/(T//4)=(4BA)/(T)`