A bar magnet of magnetic moment M is bent into a semicircular form. Its new magnetic moment will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $2M/π$
Magnetic moment of a bar magnet: $M = m \cdot l$
where $m$ is pole strength and $l$ is the pole separation (length of magnet).
When bent into a semicircle:
Original length = $l$
Arc length of semicircle = $l = \pi r \;\;\Rightarrow\;\; r = \frac{l}{\pi}$
New pole separation = chord length = $2r = \frac{2l}{\pi}$
New magnetic moment: $M' = m \cdot \frac{2l}{\pi} = \frac{2}{\pi} \, m l = \frac{2}{\pi} M$
Answer: New magnetic moment = $\frac{2}{\pi} M$