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  4. In the diagram I1,I2 are the strength of the currents in the loop and straight conductors 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 conductors is

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Q. In the diagram $I_1,I_2$ are the strength of the currents in the loop and straight conductors 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 conductors isPhysics Question Image

KCETKCET 2013Moving Charges and Magnetism

Solution:

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.
$\frac{\mu_{0} l_{1}}{2 R}=\frac{\mu_{0} l_{2}}{2 \pi(2 R)}$
$ \Rightarrow \frac{l_{1}}{l_{2}}=\frac{1}{2 \pi}E$