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

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,
$M=iA$
$M=i\cdot \pi r^2\Rightarrow =i\pi \cdot {\left(\frac{l}{2\pi }\right)}^2$
$=i\pi \cdot \frac{l^2}{4{\pi }^2}$
$\Rightarrow M=\frac{i{l}^2}{4\pi }$
$l^2=\frac{4M\pi }{i}$
$\Rightarrow l=\sqrt{\frac{4\pi M}{i}}$