(a) From Biot-Savart’s law, the magnetic induction due to a circular current carrying wire loop at its centre is given by,

The plane spiral is made up of concentric circular loops, having different radii, varying from a to b. Therefore, the total magnetic induction at the centre,

where is the contribution of one turn of radius r and dN is the number of turns in the interval (r, r + dr)

i.e.

Substituting in equation (1) and integrating the result over r between a and b, we obtain,

(b) The magnetic moment of a turn of radius