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)/(pilr)`
B. `(mg sin theta)/(pil)`
C. `(mgr sin theta)/(pil)`
D. none of these

Answer

A

Explanation

Torque due to magnetic force = tarque due to gravitational force.
`or" "MB sin ( 180- theta) = mgrsin theta `
`or " "MB sin theta = mgr sin theta `
`therefore" " B=(mgr)/(M)=(mgr)/(lpir^(2))=(mg)/(lpir^(2))`