A coil having N turns and area A is rotating in uniform magnetic field then at time t, the magnetic flux associated with the coil is given by `phi=NAB cos omegat` . In the first rotation at time t = . . s, the induced emf is obtained maximum.

Options

A. `T/2`
B. `T/8`
C. `T/4` and `(3T)/4`
D. `T/16`

Answer

C

Explanation

`phi=N AB cos omegat`
`(dphi)/(dt)=-N AB omega sin omegat `
`therefore -V=-N AB omega sin omegat`
`therefore V=N AB omega sin omegat` …(1)
If sin `omegat= 1 rArr V=V_m`
`therefore V_m = NAB omega`
`therefore` From eq. (1)
`V=V_m sin omegat`
If `V=V_m`
`1=sin omegat`
`therefore omegat =pi/2` and `(3pi)/2`
`therefore (2pi)/T xx t = pi/2` and `(2pi)/T xx t = (3pi)/2`
`therefore t=T/4` and `t=(3T)/4`