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$A$ 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
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The correct answer is:
$\frac{1}{6}$
$r_1: r_2=1: 2$ and $B_1: B_2=1: 3$ We know that
$B=\frac{\mu_0}{4 \pi} \cdot \frac{2 \pi n i}{r} \Rightarrow \frac{i_1}{i_2}=\frac{B_1 r_1}{B_2 r_2}=\frac{1 \times 1}{3 \times 2}=\frac{1}{6}$
$B=\frac{\mu_0}{4 \pi} \cdot \frac{2 \pi n i}{r} \Rightarrow \frac{i_1}{i_2}=\frac{B_1 r_1}{B_2 r_2}=\frac{1 \times 1}{3 \times 2}=\frac{1}{6}$
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