Find the vector potential above and below the plane

QUESTION:

Problem 27P

Find the vector potential above and below the plane surface current in Ex.5.8.

Reference: Ex.5.8.

Find the magnetic field of an infinite uniform surface current K = K ˆx, flowing over the xy plane

(Fig.5.33)

(one Bl comes from the top segment and the other from the bottom), so B =(μ0/2)K, or, more precisely,

Notice that the field is independent of the distance from the plane, just like the electric field of a uniform surface charge