Figure shows a coil of single turn would 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?

Explanation

Magnetic dipole of moment of the coil carrying current, `M=IpiR^2`
Its direction is perpendicular to the plane acting upwards. Resolving `vecB` into two rectangular components, we have `B cos theta` acting `_|_r` to the plane downwards and `B sin theta` acting along the plane downwards, Fig.
For rotational equilibrium of sphere about point P is
`(mg sin theta)R=M(B sin theta)` or `mg R sin theta=IpiR^2Bsintheta` or `B=(mg)/(piIR)`