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 $