Conducting planes in air at z = 0 and z = d carry surface currents of ±K₀a_x A/m.

(a) Find the energy stored in the magnetic field per unit length (0 < x < 1) in a width w(0 < y < w).

(b) Calculate the inductance per unit length of this transmission line from W_H = 1/2 LI², where I is the total current in a width w in either conductor. 

(c) Calculate the total flux passing through the rectangle 0 < x < 1, 0 < z < d, in the plane y = 0, and from this result again find the inductance per unit length.