Find the magnetic dipole moment of the spiral of total number of turns`N`, carrying current `i` having inner and outer radii `a` and `b` respectively.

Explanation

Let us take a thin coil of thickness dr. Then the number of turns of the coil is dN ` = (N)/(b-a) dr`

the dipole moment of the coil is
`M = (dN) (i)(A) = ( (Ndr)/(b-a) )(i)(pir^2) = (piNi)/(b-a) int_a^b r^2 dr`
`M = pi iN)/(3) (a^2 + ab + b^2)`