Question

5. The force on a dipole m in a magnetic field is given by F-E(, B). Show that the energy of a magnetic dipole in a magnetic field is U m B. Hint: Assume that the magnetic field is zero at infinity and imagine bringing the dipole from infinity to a point in the field.

Answer 1

We know that,

$\vec{F}=-\vec{\nabla} U.............(1)$

where F is force and U is potential energy.

And it is given in the question, the force on the dipole is

$\vec{F}=\vec{\nabla}( \vec{m}\cdot \vec{B}).............(2)$

on comparing equations 1 and 2 we get,

m B