An iron bar of length $L$ has a magnetic moment $M$. It is bent exactly at the middle of its length

Question

An iron bar of length $L$ has a magnetic moment $M$. It is bent exactly at the middle of its length such that the two arms make an angle of $90^{\circ}$ with each other. The magnetic moment of this new magnet is:

Professor PC Thomas Classes · Answer

(d) : Let $m$ be the pole strength of the bar magnet. The initial magnetic moment is $M = m 	imes L$. When it is bent at the middle at an angle of $90^{\circ}$, it forms a right-angled triangle where the two arms have lengths $L/2$. The effective distance between the two poles is the hypotenuse, $L' = \sqrt{(L/2)^2 + (L/2)^2} = \sqrt{2(L^2/4)} = \frac{L}{\sqrt{2}}$. The new magnetic moment is $M' = m 	imes L' = m \left(\frac{L}{\sqrt{2}}ight) = \frac{M}{\sqrt{2}}$.