$A$ 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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(a) ${r_1}:{r_2} = 1:2$ and ${B_1}:{B_2} = 1:3$ We know that
$B = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi ni}}{r} \Rightarrow \frac{{{i_1}}}{{{i_2}}} = \frac{{{B_1}{r_1}}}{{{B_2}{r_2}}} = \frac{{1 \times 1}}{{3 \times 2}} = \frac{1}{6}$
$B = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2\pi ni}}{r} \Rightarrow \frac{{{i_1}}}{{{i_2}}} = \frac{{{B_1}{r_1}}}{{{B_2}{r_2}}} = \frac{{1 \times 1}}{{3 \times 2}} = \frac{1}{6}$
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