A tightly wound solenoid of length l and cross sectional area `A_(1)` is partly inserted co-axially into another tightly wound solenoid of length l and cross section `A_(2) (gt A_(1))`. The centres of the two solenoids are separated by `x (lt l)`. Assume that `A_(2) lt lt x^(2), A_(2) lt lt l^(2)`. Calculate the total magnetic field energy inside the solenoid when both of them carry same current (I) in the same sense. Number of turns in each solenoid is N.

Answer

`(mu_(0)I^(2)N^(2))/(2l^(2)) [3A_(1) - 2A_(1)x +A_(2)l]`