Two circular current loops are centered on the z axis at z = ± h. Each loop has radius a and carries current I in the a_ϕ direction.

(a) Find H on the z axis over the range −h < z < h. Take I = 1 A and plot |H| as a function of z/a if

(b) h = a/4;

(c) h = a/2;

(d) h = a. Which choice for h gives the most uniform field? These are called Helmholtz coils (of a single turn each in this case), and are used in providing uniform fields.