Derive an expression for the torque on an electric dipole placed in a uniform electric field. When is the dipole in stable equilibrium?

1. 1 · Set up and draw. [Uniform field lines; dipole AB at angle θ; qE on +q along E, qE on −q against E; arm 2a sin θ marked]
2. 2 · Find the net force. +qE and −qE are equal and opposite, so the net force is zero.
3. 3 · Identify the couple. The two forces act along different lines, so they form a couple that turns the dipole.
4. 4 · Find the torque. τ = qE × 2a sin θ = pE sin θ; in vector form τ = p × E.
5. 5 · State the equilibrium. τ = 0 at θ = 0° (stable) and at θ = 180° (unstable). At 0°, a small turn brings the dipole back.
6. 6 · Close in one line. A uniform field only turns a dipole; it lines p up with E.

Scoring tip: Name the 'couple' and mark the arm 2a sin θ on your figure. Both are marking-scheme points.