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=`(mu_0IR^2N ) /(2(x^2+R^2)^(3/2))`
(i) Show that this reduces to the familiar result for field at the centre of the coil.
(ii) 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 0.72( mu_0NI)/ R ` ,
approximately. [Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.] @@@