Deduce the expression for the torque acting on a magnetic dipole placed in a uniform magnetism field?

Explanation

Consider NS be a bar magnet of length 2l and strength of each pole = m. The magnet is held at `angle theta` with the direction of magnetic field B.

Force on N pole = mB, along B
Force on S pole = mB, opposite to B
where, m = strength of each pole and
and B = magnetic field induction.
These equal and unlike forces form a couple which tend to rotate the magnet clockwise, so as to align it along B.
Torque acting on the bar magnet,
`tau` = Force `xx` Perpendicular distance
`tau=mBxxNA`
In `DeltaNAS, sintheta=(NA)/(NS)=(NA)/(2l)`
`NA=2lsintheta`
Now, `tau=mBxx2lsintheta`
`=Bxx(m2l)sintheta`
`tau=MBsintheta`