Magnetic Potential Energy

A magnetic dipole moment in a magnetic field will possess potential energy which depends upon its orientation with respect to the magnetic field. Since magnetic sources are inherently dipole sources which can be visualized as a current loop with current I and area A, the energy is usually expressed in terms of the magnetic dipole moment:

where

The energy is expressed as a scalar product, and implies that the energy is lowest when the magnetic moment is aligned with the magnetic field. The difference in energy between aligned and anti-aligned is

where ΔU = 2μB

The expression for magnetic potential energy can be developed from the expression for the magnetic torque on a current loop.

These relationships for a finite current loop extend to the magnetic dipoles of electron orbits and to the intrinsic magnetic moments associated with electron spin and nuclear spin.