Question

A magnetised wire of magnetic moment $M$ is bent at the middle and two parts are at an angle of ${90}^o$. Find resultant magnetic moment.

Answer 1

$\frac{M}{\sqrt{2}}$

Let the length of the wire be $L$

If the wire is bent at the middle, then each part will have length $\frac{L}{2}$

The straight distance between the end points will be given by applying pythagoras theorem.

$=\sqrt{{\left(\frac{L}{2}\right)}^2+{\left(\frac{L}{2}\right)}^2}=\frac{L}{\sqrt{2}}$

Magnetic moment of any dipole, is directly proportional to the straight distance between the poles.

Hence the new moment is given by $M^{\prime }=\frac{M\times L}{L\times \sqrt{2}}=\frac{M}{\sqrt{2}}$