A rectangular coil of single trun, having area `A` , rotates in a uniform magnetic field `B` with an angular velocity `omega` about an axis prependicular to the field. If initially the plane of the coil is perpendicular to the field, then the average induced emf when it has rotate through `90^(@)` is

Options

A. `(omegaBA)/(pi)`
B. `(omegaBA)/(2pi)`
C. `(omegaBA)/(4pi)`
D. `(2omegaBA)/(4pi)`

Answer

D

Explanation

At `t=0` , `phi=Bacos0=NBA`
`t=(pi//2)/(omega),phi=BAcos90^(@)=0`
`|bar(e)|=(Deltaphi)/(Deltat)=(BA)/((pi//2)/(omega))`
`=(2BAomega)/(pi)` .