Question

A straight magnetised wire of magnetic moment '$M$' is bent into shape as shown. Find final magnetic moment.

Answer 1

$\frac{M}{\sqrt{5}}$

As shown in the figure, the wire is bent into 5 equal parts.

So if L is the lengthof the wire, then length of each part is L/5.

We have to find the magnetic moment between points A and B.

As per pythagoras theorem, the length of AB is given by

$AB=\sqrt{B{C}^2+A{C}^2}$

But $BC=\frac{L}{5}$ and $AC=\frac{2L}{5}$

$\therefore AB=\sqrt{{\frac{L}{25}}^2+{\frac{4L}{25}}^2}=\frac{L}{\sqrt{5}}$

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

Hence the new moment is given by $M^{\prime }=\frac{M\times L}{L\times \sqrt{5}}=\frac{M}{\sqrt{5}}$