A circular coil with radius 10 cm and 10 no. of tightly wound identical turns is kept perpendicular to uniform magnetic field `2 xx 10^(-4)`G intensity. Now, it is rotated with angular velocity `2pi "rad s"^(-1)` about an axis passing through it but perpendicular to magnetic field. Then, at ........s, least time magnetic flux passing through it becomes half of maximum magnetic flux.

Options

A. `1/2`
B. `1/12`
C. `1/6`
D. `1/4`

Answer

C

Explanation

We have `Phi=NAB cos (omegat)`…(1)
`therefore Phi=Phi_"max" cos (omegat)`…(2)
(Where `Phi_"max"` = maximum magnetic flux passing through the coil )
Now , we are given `Phi=1/2Phi_"max"`
`therefore 1/2 Phi_"max"=Phi_"max" cos (omegat)`
`therefore cos (omegat)=1/2`
`therefore omegat =pi/3`
`therefore (2pi)t=pi/3`
`therefore t=1/6s`