In Fig. a coil of single turn is wound on a sphere of radius r and mass m. The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equilibrium, the value of B is [Current in the coil is i]

Options

A. `(mg)/(piir)`
B. `(mgsintheta)/(pii)`
C. `(mgrsintheta)/(pii)`
D. none of these

Explanation

The gravitational torque must be counter balanced by the magnetic torque about `O`, for equilibrium of the sphere. The gravitational torque
`tau_(gr)=mgr sintheta`
The magnetic torque `tau_(m)=vecmuxxvecB`
Where the magnetic moment of the coil `=mu=(ipir^(2))`
`rArrtau_(m)=pi ir^(2)B sin theta`
`pi i r^(2) B sintheta=mgrsintheta`
`rArr B=(mg)/(pi i r)`