Question

A current $i$ is flowing in a conductor of length $l$. When it is bent in the form of a loop its magnetic moment will be

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

Answer 1

The correct option is B $\frac{i{l}^2}{4\pi }$

When the wire of length $l$ is bent to form a loop of radius $r$

$r=\frac{l}{2\pi }$

Area of the loop $A=\pi r^2=\pi {\left(\frac{l}{2\pi }\right)}^2$
Magnetic moment: $\mu =iA=i\pi \frac{l^2}{4{\pi }^2}=\frac{i{l}^2}{4\pi }$