The magnetic field intensity is given in a certain region of space as H = [(x + 2y)/z²]a_y + (2/z)a_z A/m.

(a) Find ∇× H.

(b) Find J.

(c) Use J to find the total current passing through the surface z = 4, 1 ≤ x ≤ 2, 3 ≤ z ≤ 5, in the a_z direction.

(d) Show that the same result is obtained using the other side of Stokes’ theorem.