(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 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 : `P = (dW)/(dt) = |epsilon|` I (since power `P=VI` )
But we know that , `epsilon = L (dI)/(dt)`
Therefore, `(dW)/(dt) = L I (dI)/(dt) rArr dW = LI dI`
Therefore, the total work done in establishing a current I is given by `W = int d W = int_(0)^(1) L I d I = ""_(1//2)LI^(2)`
This work is stored in the coil in the form of magnetic potential energy, `U= 1/2 L I^(2)`