Give the expression for energy stored in an inductance coil carrying current.

Explanation

When a current is established in a solenoid (coil), work has to be done against the back emf. This work done is stored in the form of magnetic energy in the coil .
For a current I in the coil , the rate of work done (power) is `(dw)/(dt)=epsilonI`
But we know that : `epsilon=L (dI)/(dt)`
`rArr dw=LIdI`
Therefore work done in establishing a current I is given by
`w=int dw= int LIdI=1/2LI^2`
This work is stored in the coil in the form of energy .
Therefore , the energy in a coil is given by `U=1/2LI^2`