A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field `Bhati`. The torque on the coil due to the magnetic field is :

Options

A. `(Br^2 I)/(pi N)`
B. zero
C. `(B pi r^2 I)/(N)`
D. `B pi r^2 N`

Answer

D

Explanation

Coil lies on the XZ plane hence its magnetic moment (M=NIA) will be along the Y-axis. Magnetic field is applied along the X-axis hence angle between magnetic moment and magnetic field is `90^@` . So torque acting on the coil can be written as follows:
`tau = MB sin theta 90^@ = MB =NIAB = NI (pi r^2) B = B pi r^2 IN`