Question

A wire of length 'L' meters carrying a current'i amperes is bent in the form of a circle. The magnitude of its magnetic moment is

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

Answer 1

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

Given : A wire of length L is bent in form of circle carrying current i.

$2\pi r=L$ $\Rightarrow$ $r=\frac{L}{2\pi }$

Solution:

We have formula for magnetic moment as M=iNA

i=current , N= number of turns, A=area of loop

Substituting all the value s in the formula we get

$M=i\times 1\times \pi r^2$

$M=i\times \pi \left(\frac{L^2}{4\pi }\right)$

$M=\frac{i{L}^2}{4\pi }$

The correct opt is B