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. `(omega BA)/(pi)`
B. `(omega BA)/(2pi)`
C. `(omega BA)/(4pi)`
D. `(2omega BA)/(pi)`

Answer

D

Explanation

Initially flux, `phi = BA cos 0 = BA`
After rotating through an angle `90^(@)`.
Flux through the coil is zero. So, `Delta phi = BA`
Angular speed = w, so, time period `=(2pi)/(omega)=T`
`(T)/(4)` is time taken to rotate `90^(@)`.
So, `(Delta phi)/(Delta t)=(BA)/(T//4)=(2BA omega)/(pi)`