Problem 3.345

Demonstrate that the magnetic energy of interaction of two current-carrying loops located in vacuum can be represented as \(W_{i a}=\left(1 / \mu_{0}\right) \int \mathbf{B}_ {1} \mathbf{B}_ {2} d V,\) where \(\mathbf{B}_ {1}\) and \(\mathbf{B}_ {2}\) are the magnetic inductions within a volume element \(d V\), produced individually by the currents of the first and the second loop respectively.