Two different small circular copper coils have a radii ratio of $1 : 2$. If the currents flowing thr

Question

Two different small circular copper coils have a radii ratio of $1 : 2$. If the currents flowing through them are in the ratio $2 : 3$ respectively, the ratio of their respective magnetic moments will be

Professor PC Thomas Classes · Answer

(b) :  The magnetic moment of a circular coil is given by $M = IA = I \pi r^2$. Therefore, the ratio of their magnetic moments is $\frac{M_1}{M_2} = \left(\frac{I_1}{I_2}ight) 	imes \left(\frac{r_1}{r_2}ight)^2$. Substituting the given ratios, we get $\frac{M_1}{M_2} = \left(\frac{2}{3}ight) 	imes \left(\frac{1}{2}ight)^2 = \frac{2}{3} 	imes \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$. Thus, the ratio is $1 : 6$.