A bar magnet is placed in a uniform magnetic field. Write expressions for the torque on it and its potential energy. Explain the positions of stable and unstable equilibrium.

1. 1 · Net force. The forces on the poles are equal and opposite, so the net force is zero; they form a couple.
2. 2 · Draw. [Uniform field lines; magnet at angle θ; forces along and against B at N and S; m and θ marked]
3. 3 · Torque. τ = m × B, size mB sin θ; largest (mB) at θ = 90°.
4. 4 · Energy. U = −m·B = −mB cos θ.
5. 5 · Equilibrium.
   • θ = 0°: τ = 0, U = −mB, stable.
   • θ = 180°: τ = 0, U = +mB, unstable.
6. 6 · Close in one line. So, the torque always tries to line m up with B, as a compass needle shows.

Scoring tip: Give both equilibrium positions with their energies. The sign of U decides which one is stable.