Question

A straight wire of length l and magnetic moment m is bent into shape of semicircle, then what will be new magnetic moment?

Answer 1

We know that, pole strength $m=\frac{M}{l}$
If r is the radius of semicircle formed by bending a wire of length l.
then, $\pi r=l$
$r=\frac{1}{\pi }$
Distance between the poles, $2r=\frac{2l}{\pi }$
Hence, New magnetic moment $\left(m^{\prime }\right)$
$m^{\prime }=\frac{M}{l}\cdot \frac{2l}{\pi }=\frac{2M}{\pi }$.