Question

A straight wire carrying current ' $i$ ' is turned into a circular loop. If the magnitude of magnetic moment associated with it in $M . K . S$. units is $M$. the length of wire will be________

• A. $4 \pi i M$
• B. $\sqrt{\frac{4 \pi M}{i}}$
• C. $\sqrt{\frac{4 \pi i}{M}}$
• D. $\frac{m \pi}{4 i}$

Answer 1

Answer: (B)

Suppose, $l$ be the length of wire.
Hence, $l=2 \pi r$
$\Rightarrow r=\frac{l}{2 \pi}$
$\therefore $ Magnetic dipole moment,
$M=i A$
$M=i \cdot \pi r^{2} \Rightarrow =i \pi \cdot\left(\frac{l}{2 \pi}\right)^{2}$
$=i \pi \cdot \frac{l^{2}}{4 \pi^{2}}$
$\Rightarrow M=\frac{i l^{2}}{4 \pi}$
$l^{2}=\frac{4 M \pi}{i}$
$\Rightarrow l=\sqrt{\frac{4 \pi M}{i}}$