Question

A circular coil of closely wound N turns and radius r carries a current I. If the expression of the magnetic moment of this coil is given by $\mu =iN\pi R^a$. find a.

Answer 1

Magnetic field at the center of the loop using Biot-Savart Law

$\overrightarrow{B}=\frac{{\mu }_{0}Ni}{4\pi }\oint \frac{dl}{R^2}$

$=\frac{{\mu }_{0}Ni}{4\pi }\times 2\pi R/R^2$

$=\frac{{\mu }_{0}Ni}{2R}$

Hence the magnetic moment of the coil is $=\mu =iNA=iN\pi R^2$