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 P30.55.
(a) Show that the magnetic field on the axis at a distance x from the center of one coil is
(b) Show that dB/dx and d 2B/dx 2 are both zero at the point midway between the coils. This means the magnetic field in the region midway between the coils is uniform. Coils in this configuration are called Helmholtz coils.

NuoIR? 1. 1 (R + x*)3/2 (2R2 + x - 2Rx)3/2