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In the diagram, $I_{1}, I_{2}$ are the strength of the currents in the loop and straight conductors respectively. $O A=A B=R$. The net magnetic field at the centre $O$ is zero. Then the ratio of the currents in the loop and the straight conductos is
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The correct answer is:
$\frac{1}{2 \pi}$
Given that the net magnetic field at the centre $O$ is zero. Therefore, magnetic field at $O$ due to circular coil and straight conductor must be equal and opposite in direction.
$\therefore \quad \frac{\mu_{0} l_{1}}{2 R}=\frac{\mu_{0} I_{2}}{2 \pi(2 R)} \Rightarrow \frac{I_{1}}{I_{2}}=\frac{1}{2 \pi}$
$\therefore \quad \frac{\mu_{0} l_{1}}{2 R}=\frac{\mu_{0} I_{2}}{2 \pi(2 R)} \Rightarrow \frac{I_{1}}{I_{2}}=\frac{1}{2 \pi}$
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