Figure shows a coil of single turn wound on a sphere of radius R and mass m. The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere. What is the value of B if the sphere is in equilibrium when current in the coil is I?

Options

A. `(m g cos theta)/(pi iR)`
B. `(mg)/(pi iR)`
C. `(m g tan theta)/(pi i R)`
D. `(m g sin theta)/(pi i R)`

Answer

B

Explanation

The gravitational torque must be counter balanced by magnetic torque about O. for equilibrium of the sphere. The gravitational torque
`impliesT_(m)=piR^(2)iB sin theta`……….1
`T_(mg)=mgR sin thetaimpliespiR^(2)iB sin theta =m gr sin theta,B=(mg)/(pi ir)`