Question

A thin circular wire carrying a current I has a magnetic moment M. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment

• A. $M$
• B. $\frac{4}{{\pi }^2}M$
  
• C. $\frac{4}{\pi }M$
  
• D. $\frac{\pi }{4}M$

Answer 1

The correct option is D $\frac{\pi }{4}M$

Initially for circular coil $L=2\pi r$ and $M=i\times \pi r^2$
$=i\times \pi {\left(\frac{L}{2\pi }\right)}^2=\frac{i{L}^2}{4\pi }$ ..... (i)
Finally for square coil $M^{\prime }=i\times {\left(\frac{L}{4}\right)}^2=\frac{i{L}^2}{16}$ ..... (ii)


Solving equation (i) and (ii) $M^{\prime }=\frac{\pi M}{4}$