Q. A short magnet placed with its axis making an angle with a uniform external magnetic field of induction B experiences a torque (τ). If the magnet is free to rotate, which orientation would correspond to its stable and unstable equilibrium.

(a) θ = 0°, θ= 90°

(b) θ = 0°, θ = 180°

(c) θ = 45°, θ = 135°

(d) θ = 0°, θ = 270°

Ans: (b)

Sol: Potential Energy $ \displaystyle U = – M B cos\theta $

For stable equilibrium; U = minimum , θ = 0°

$ \displaystyle U_{min} = – M B cos0 = – M B $

For unstable equilibrium; U = maximum , θ = 180°

$ \displaystyle U_{max} = – M B cos180 = + M B $