Calculate potential energy of a magnetic dipole in a magnetic field.

Explanation

Let a magnetic dipole NS be placed in uniform magnetic field `vecB` at an angle `theta` with the field.

Force on N-pole = `mB("along"vecB)`
Force on S-pole = mB (opposite to `vecB`)
Torque acting on the bar magnet.
i.e., `tau=mB(bot"distance "NS)`
or `tau=mB(NA)`
But `NA=2lsintheta`
`therefore" "tau=mB2lsintheta=m2lBsintheta`
or `tau=MBsintheta" "[becauseM=2l]`
or `vectau=vecMxxvecB`
`vectau` is perpendicular to the plane containing `vecMandvecB`.
If `theta=90^(@),B=1`, then
`tau=Mxx1xx1`
or `M=tau`
Therefore magnetic dipole moment is defined as the torque experienced by the dipole placed perpendicular to uniform magnetic field of unit strength.
S.I. unit of `vecM` is `JT^(-1)` (joule per tesla).