Question

The magnetised wire of moment $M$ and length $l$ is bent in the form of semicircle of radius $r$. Then its magnetic moment is

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

Answer 1

Answer: (C)

$\frac{M}{\pi}$

Answer 2

Use the formula of the magnetic moment of a bar magnet. Step 1: Write the expression of the initial magnetic moment. We have length $=1$, Magnetic moment $= M$ Therefore $M = ml ;$ where $m =$ pole strength Step 2: Calculate the final magnetic moment. Now wire of length 1 changes to semicircle (Let radius is $r$ ) therefore $1=\pi r$ $\Rightarrow r =\frac{1}{\pi}$ Now new magnetic moment $M'=M \times 2 r=\frac{2 m l}{\pi}=\frac{M}{\pi}$