Q: Two circular coils are made from a uniform wire the ratio of radii of circular coils are 2:3 & no. of turns 3:4. If they are connected in parallel across a battery.

(a) find ration of magnetic inductions at their centres

(b) find the ratio magnetic moments of 2 coils.

Sol: (a) when connected in parallel

$\large B \propto \frac{1}{r^2}$

$\large \frac{B_1}{B_2} = (\frac{r_2}{r_1})^2 $

$\large \frac{B_1}{B_2} = (\frac{3}{2})^2 = \frac{9}{4}$

(b) $\large M = n i A_c $ , but $\large i = \frac{V}{R} = \frac{V}{\rho l} A_w $

$\large M = \frac{V A_w}{\rho (2 \pi r)} (\pi r^2)$

$\large \frac{M_1}{M_2} = \frac{r_1}{r_2} = \frac{2}{3} $