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. `(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)`