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

Moment of the bar magnet , `M=0.32JT^(-1)`
External magnetic field, `B=0.15T`
(a) The bar magnet is aligned along the magnetic field. This sytem is considered as being in stable equilibrium, Hence, the angle `theta`, between the bar magnet and the magnetic field is `0^(@)`.
Potential energy of the system `=-M B cos theta`
` =-0.32xx0.15cos0^(@)`
`=-4.8xx10^(-2)J`
(b) The bar magnet is oriented `180^(@)` to the magnetic field. Hence it is in unstable equilibrium .
`theta=180^(@)`
Potential energy =`-MB cos theta`
` - 0.32xx0.15 cos 180^(@)`
`=4.8xx10^(-2)J`