# Two circular coils are made from a uniform wire the ratio of radii of circular coils are 2:3 and no. of turns is 3:4. If they are connected in parallel across a battery. Find ratio of magnetic inductions at their centres.

Eshan
$B=\dfrac{\mu_0Ni}{2R}$
$\implies \dfrac{B_2}{B_1}=\dfrac{N_2}{N_1}\times \dfrac{I_2}{I_1}\times\dfrac{R_1}{R_2}$
Also the ratio of resistances will be$\dfrac{r_2}{r_1}=\dfrac{l_2}{l_1}=\dfrac{N_2(2\pi R_2)}{N_1(2\pi R_1)}$,
$\implies \dfrac{I_2}{I_1}=\dfrac{r_2}{r_1}=\dfrac{N_1R_1}{N_2R_2}$