The magnetic moment of a straight iron bar is $M$. It is now bent into a perfect semicircle. The mag

Question

The magnetic moment of a straight iron bar is $M$. It is now bent into a perfect semicircle. The magnetic moment of this semicircular magnet is

Professor PC Thomas Classes · Answer

(b) : Let $L$ be the initial length and $m$ be the pole strength, so $M = mL$. When bent into a semicircle of radius $r$, the arc length equals the original length, so $\pi r = L$, meaning $r = L/\pi$. The new distance between the magnetic poles is the diameter of the semicircle, which is $2r = 2L/\pi$. The new magnetic moment $M' = m 	imes (2r) = m 	imes \left(\frac{2L}{\pi}ight) = \frac{2M}{\pi}$.