Question

$A$ and $B$ are the two concentric circular conductors of center $O$ 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

• A. $1 / 6$
• B. $1 / 4$
• C. $1 / 3$
• D. $1 / 2$

Answer 1

Answer: (A)

$r_{1}: r_{2}=1: 2$ and $B_{1}: B_{2}=1: 3$ (flux density)
$B =\frac{\mu_{ o }}{4 \pi} \frac{2 \pi nI }{ R }$
$\frac{I_{1}}{I_{2}}=\frac{B_{1}}{B_{2}} \frac{R_{1}}{R_{2}}=\frac{1 \times 1}{3 \times 2}=\frac{1}{6}$
$\frac{I_{1}}{I_{2}}=\frac{1}{6}$