Q81 / 120 · VITEEE 2010 · Physics

A straight wire carrying current $i$ is turned into a circular loop. If the magnitude of magnetic moment associated with it in MKS unit is $M$, the length of wire will be

  • A
    $\frac{4 \pi}{\mathrm{M}}$
  • Correct answer
    B
    $\sqrt{\frac{4 \pi M}{i}}$
  • C
    $\sqrt{\frac{4 \pi i}{\mathrm{M}}}$
  • D
    $\frac{M \pi}{i}$

Solution

Here, length $l=2 \pi r$ or $r=\frac{1}{2 \pi}$ Area of circular loop $A=\pi r^{2}$ Magnetic moment $M=i A=i \pi r^{2}$ $$ \begin{array}{l} M=i \pi \times \frac{l^{2}}{4 \pi^{2}} \\ \therefore l=\sqrt{\frac{4 \pi M}{i}} \end{array} $$

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

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