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_(0) IR^(2)N)/(2(x^(2)+R^(2))^(3//2))`
a) Show that this reduces to the familiar result for field at the centre of the coil.

Explanation

Given, magnetic field at distance x
`B=(mu_(0) NIR^(2))/(2(x^(2)+R^(2))^(3//2))" "(because x=0)`
`therefore` The magnetic field at the centre `B=(mu_(0)NIR^(2))/(2R^(3))`
`B=(mu_(0)NI)/(2R)`.
The result is same as the magnetic field due to current loop at its centre.