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. unit 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)

$\sqrt { \frac { 4 \pi M } { i } }$

Answer 2

Magnetic moment of circular loop carrying current

$M = I A = I \left( \pi R ^ { 2 } \right) = I \pi \left( \frac { L } { 2 \pi } \right) ^ { 2 } = \frac { I L ^ { 2 } } { 4 \pi } \Rightarrow L = \sqrt { \frac { 4 \pi M } { I } }$