A short bar magnet of moment `0*32JT^-1` is placed in a uniform external magnetic field of `0*15T`, if the bar is free to rotate in the plane of the field, which orientations would correspond to its, (i) stable and (ii) unstable equilibrium? What is the potential energy of the magnet in each case?

Explanation

Given, magnetic moment `m=0.32 JT^(-1)` and magnetic field B = 0.15 T
(i) If `vecm || vecB , i.e. theta = 0^@` , then we have stable equilibrium because potential energy is minimum in this case, and the potential energy of the magnet in this case is given by:
` U = -m B cos 0^@`
` = -0.32 xx 0.15 T`
` = -4.8 xx 10^(-2) J`
(ii) If `vecm` is anti-parallel to `vecB` , i.e. `theta = 180^@` , then we have unstable equilibrium due to maximum potential energy, and the potential energy of the magnet in this case is given by:
` U = - mB cos 180^@`
` = 0.32 xx 0.15T`
` = 4.8 xx 10^(-2) J`