Consider two poles arranged directly opposite each other as shown in Fig. 29. Let each have an area A square meters and F Newtons be the force of alteration between them. Let one pole be moved by an incremental distance \(\delta x\) against the force F then the work done is obviously F\(\delta x\) Juoules.

The volume of the magnetic field between the poles is increased by A\(\delta x\)m³

Fig.29

Hence the energy stored increased by

Energy density of the magnetic field \(\times\)A\(\delta x\) Joules

Or \(F\delta x=\frac{1}{2}\left(\frac{B^2A}{\mu_0\mu}\delta x\right)Joules\)

Energy is stored in the air gap.

Hence \(\mu=1\)

\(F=\frac{B^2A}{{2\mu}_0}\)