In the figure shown a coil of single turns is would on a sphere of radius R and mass m .The palne the coil is parallel to the planes and lies in the equatorial plane of the sphere . Current in the coil is i. The vaule of B if the sphere is in equailibrum is

Options

A. `(mg)/(pi ir)`
B. `(mg sin theta)/(pi i)`
C. `(mg sin theta)/(pi i)`
D. None of these

Answer

a

Explanation

The gravitational torque must be counter balanced by the magnetic torque about O, for equilibrium of the sphere.
The gravitational torque `tau_m=piir^2B`
`sin theta`
`:. Pi ir^2B sin theta=mgr sin theta`
`implies B=(mg)/(piir)`
.