For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x
from its centre is given by,
B=μ0IR2N2(x2+R2)3/2
(a) Show that this reduces to the familiar result for field at the centre of the coil.(b) Consider two parallel co-axial circular coils of equal radius R,and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by.
B=0.72μ0NIR
[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]