Obtain an expression for magnetic potential energy of a magnetic dipole placed in an uniform magnetic field.

Explanation

Let M be the magnetic pole strength. Let B be the uniform magnetic field. Let NS represent magnetic between dipole of length `2l`. Let `theta` be the angle between the magnetic axis and the magnetic field. The magnetic force on the north pole is MB and that on the south pole is - MB. The torque acting on the magnetic dipole = `tau = MB xx` perpendicular distance between the two parallel forces. From the figure sin `theta = (AC)/(AB)` . So that AC = AB sin `theta = 2 l sin theta` . Torque = `tau = MB 2l sin theta. ` But magnetic dipole moment m = `2l` M.
`tau = mB sin theta` , Work done by torque on the dipole - W - `int tau d0`
i.e., W = `int m B sin theta d theta = - m B cos theta`
This work done is stored in the form of potential energy . P.E. = `-mB cos theta = vecm.vecB.`