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 `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)underset(a)overset(b)int r^(2)dr`
`M=(piiN)/(3)(a^(2)+ab+b^(2))`.