(a) Obtain the expression for the magnetic energy stored in a solenoid in terms of magnetic field B, area A and length l of the solenoid. (b) How does this magnetic energy compare with the electrostatic energy stored in a capacitor?

Explanation

When a current is established in a coil , work has to be done against the back emf.
This work done is stored in the form of magnetic energy in the coil.
Let dw be the work done in establishing a current I in the coil in a time dt. Then
dw=-`epsilon` I dt Where `epsilon` is induced emf.
Since `epsilon=-L(dI)/(dt)`
We have `dw=L(dI)/(canceldI)Icanceldt rArr dw=L I dI`
The total work done is establishing current is
`w=int dw = int_0^1L I dI = L[1^2/2]_0^I=1/2LI^2`
This work is stored in the coil in the form of magnetic potential energy
`U=1/2LI^2`