Q139 / 180 · KCET 2013 · Physics

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
Figure

  • A
    $\pi$
  • B
    $2 \pi$
  • C
    $\frac{1}{\pi}$
  • Correct answer
    D
    $\frac{1}{2 \pi}$

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

Hence, the correct answer is option: 'D'.

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