Question

$A$ and $B$ are two concentric circular conductors of centre $O$ and carrying currents $1_1$ and $1_2$ as shown in the figure. The ratio of their radii is $1:2$ and ratio of the flux densities at $O$ due to $A$ and $B$ is $1:3$. The value of $1_1/1_2$ will be

Answer 1

Magnetic field at center of circular coil $B=\frac{{\mu }_{o}I}{2r}$

$\therefore B\propto \frac{I}{r}$

For coil A, BA$\propto \frac{I_1}{r}$

For coil B, BB$\propto \frac{I_2}{2r}$

$\frac{BA}{BB}=\frac{I_1}{I_2}\times \frac{2r}{r}$

$\frac{1}{3}=\frac{I_1}{I_2}\times 2$

$\frac{I_1}{I_2}=\frac{1}{6}$.