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

a. Work done = Energy spent in establishing current 1 in a solenoid is `U_(B)=(1)/(2)LI^(2)`
`=(1)/(2)L((B)/(mu_(0)n))` (since `B=mu_(0)nI`, for a solenoid)
`=(1)/(2)(mu_(0)n^(2)Al)((B)/(mu_(0)n))^(2)` (from Eq. `6.9.2(3))=(1)/(2mu_(0))B^(2)Al`
b. The magnetic energy per unit volume V is,
`u_(B)=(U_(B))/(V)=(U_(B))/(Al)=(B^(2))/(2mu_(0))`
We have already obtained the relation for the square of the field strength.