Multiplying throughout by the current I gives

This is now an energy conservation equation,

Rate of thermal heating (I²R)  +  Rate at which energy is stored in the inductance (LI dI/dt)  =  Rate at which energy is supplied  (εI)

• The energy stored in the inductance is associated with the magnetic field of the inductance, U_B.  Therefore,

which upon integration gives

equivalent to the electrical case of energy stored in a capacitor U_E = q²/2C = (1/2)CV².

• Exactly as in the electric field case, we can determine a general expression for the energy density (u_B) stored in a magnetic field,