A magnetic dipole experiences a torque of 80√3N m when placed in uniform magnetic field ​

Question

A magnetic dipole experiences a torque of \(80 \sqrt 3\ Nm\) when placed in uniform magnetic field in such a way that dipole moment makes angle of \(60 ^ \circ\) with magnetic field. The potential energy of the dipole is :

(1) 80 J

(2) \(- 40 \sqrt3\ J\)

(3) – 60 J

(4) – 80 J

Answer 1

Correct option is : (4) – 80 J

\(\tau = M \times B = MB \sin60 = \frac{\sqrt3}{2} MB = 80 \sqrt{3}\)

MB = 160

\(U = - M.B = - MB \cos 60\)

\(U = - 160 \times \frac{1}{2} = - 80\ J\)