Question

A straight magnetised wire of magnetic moment '$M$' is bent as shown. Find resultant magnetic moment in each case.

Answer 1

Let pole strength of magnetic wire $P$ and length of wire is $l$. Then magnetic moment $M$ is

$M=Pl⟶\left(1\right)$.

When wire is bent as shown in figure

$4\left(\pi r\right)=l$

$R=\frac{l}{4\pi }⟶\left(2\right)$

Now effective length of bent wire is =$4\left(2R\right)$

Magnetic moment of bent wire is $M^{\prime }$.

$M^{\prime }=P\left(8R\right)=\frac{2Pl}{\pi }=\frac{2}{\pi }M⟶\left(3\right)$.