A magnetic dipole experiences a torque of 80 √3 N m when placed in uniform magnetic field in such a way that dipole moment makes angle of 60° with magnetic field. The potential energy of the dipole is :

Solution

Physics sir · 3 steps

Use the torque to find mB first, then switch from sin to cos for the energy.

1. Torque gives mB. Torque on a dipole is τ = mB sin θ. With θ = 60°, mB × √3/2 = 80√3, so mB = 160 N m.

   U = -mB cos θ = -160 × cos 60°

2. Put in numbers. cos 60° = 1/2, so U = -160 × 1/2 = -80 J.
3. So. The potential energy of the dipole is -80 J, option (b).

The idea to keep. Torque goes with sin θ and energy goes with -cos θ. Dividing the two gives the shortcut U = -τ cot θ.

Answer from the NTA final answer key. Solution by PrepWiser.