Q161 / 180 · KCET 2012 · Physics

In the loop shown, the magnetic induction at the point $\mathrm{O}$ is

  • A
    zero
  • B
    $\frac{\mu_{0} I}{8}\left(\frac{R_{1}-R_{2}}{R_{1} R_{2}}\right)$
  • Correct answer
    C
    $\frac{\mu_{0} \mathrm{I}}{8}\left(\frac{\mathrm{R}_{1}+\mathrm{R}_{2}}{\mathrm{R}_{\mathrm{1}} \mathrm{R}_{2}}\right)$
  • D
    $\frac{\mu_{0} \mathrm{I}}{8}\left(\frac{\mathrm{R}_{1} \mathrm{R}_{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}\right)$

Solution

Net magnetic field at $O$ $$ \begin{aligned} B &=B_{1}+B_{2}=\frac{-\pi / 2}{2 \pi}-\frac{\mu_{0} I}{2 R_{1}}+\frac{\pi / 2}{2 \pi} \cdot \frac{\mu_{0} I}{2 R_{2}} \\ &=\frac{\mu_{0} I}{8}\left(\frac{R_{1}+R_{2}}{R_{1} R_{2}}\right) \end{aligned} $$

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

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