Energy stored in a magentic system

In a magnetic system, the energy stored in the magnetic field is equal to the integral of the instantenous power, which is the product of voltage and current,
Wm = int{ei dt'}

However, the voltage corresponds to the induced emf, according to Faraday's law,
e = d lambda / dt = N d phi / dt
and is therefore
Wm = int{i d lambda}

Define a fictitious quantity called co-energy, W'm.
W'm = i lambda - Wm