Chapter 29, Problem 38AP

Two circular coils of radius R, each with N turns, are perpendicular to a common axis. The coil centers are a distance R apart. Each coil carries a steady current I in the same direction as shown in Figure P29.38. (a) Show that the magnetic field on the axis at a distance x from the center of one coil is

$B=\frac{N{\mu }_{0}I{R}^2}{2}\left[\frac{1}{{(R^2+x^2)}^{3/2}}+\frac{1}{{(2R^2+x^2-2Rx)}^{3/2}}\right]$