How Energy associated with an Inductor?

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 (I0) is

w= ∫dw= l0 −L I dI

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

∴ Energy stored in the coil

= −L l0 IdI = – ½ . L I02

Negative sign is consequence of Lenz’s Law. Hence, quantitatively, the energy stored in an inductor is: ½.L I02