In the diagram, $I_1$ , $I_2$ are the strength of the currents in the loop and infinite long straight conductor respectively. $OA = AB = R$ . The net magnetic field at the centre $O$ is zero. Then the ratio of the currents in the loop and the straight conductor is
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$\frac{\mu_{0} \mathrm{I}_{1}}{2 \mathrm{R}}=\frac{\mu_{0} \mathrm{I}_{2}}{2 \pi(2 \mathrm{R})}$
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