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} $