Question

$A$ and $B$ are two concentric circular conductors of centre $O$ and carrying currents $I_1$ and $I_2$ as shown in the adjacent figure. If ratio of their radii is $1:2$ and ratio of the flux densities at $O$ due to $A$ and $B$ is $1:3$, then the value of $I_1/I_2$ is:

Answer 1

$B=\frac{{\mu }_{o}I}{2R}$

$\frac{I_1}{I_2}=\frac{B_1{R}_1}{B_2{R}_2}$

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

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