The magnetic field strength in a long superconducting soleno

The magnetic field strength in a long superconducting solenoid buried underground in Switzerland is 15.0 T. The cross sectional area of the solenoid is 3.0 times 10^4 m^2, and its length is approximately 40 km. If a loss of cooling allows the superconducting wires to suddenly become normal, so that B drops to zero, how much energy will be released as heat?

Solution

A =3*10^-4 m^2, B =15 T, L =40 km, uo = 4pi*10^-7 T.m/A

energy density u = B^2/2uo

U/V = B^2/2uo

U/(3*10^-4*40000) = (15*15)/(2*4*3.14*10^-7)

U = 1.075*10^9 J