Whenever current flows through a coil, the self−inductance opposes the growth of the current. Hence, some work has to be done by external agencies in establishing the current. If e is the induced emf then,

**e = – L (dI/dt)**

The small amount of work dw done in a time interval dt is

**dw = e.I dt**

**= −L (dI/dt) I.dt**

The total work done when the current increases from 0 to maximum value (I_{0}) is

**w= ∫dw= ^{l}∫_{0} −L I dI**

This work done is stored as magnetic potential energy in the coil.

∴ Energy stored in the coil

**= −L ^{l}∫_{0} IdI = – ½ . L I_{0}^{2}**

Negative sign is consequence of Lenz’s Law. Hence, quantitatively, the energy stored in an inductor is: **½.L I _{0}^{2}**