A bar magnet with pole strength m and magnetic dipole moment p is cut into two identical pieces along its length. Then for each of the two pieces
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → pole strength and dipole moment are m/2 and p/2, respectively
The pole strength of a magnet is proportional to the area of cross-section of its pole faces, and the dipole moment is pole strength times the magnetic length.
\( p = m \times 2l \)
A cut along its length (parallel to the axis) gives two pieces of the full length \( 2l \), each with half the cross-section.
\( \displaystyle m' = \frac{m}{2}, \qquad p' = \frac{m}{2} \times 2l = \frac{p}{2} \)
Option (1) pole strength and dipole moment are m and p, respectively — Incorrect. Each piece has only half the cross-section.
Option (3) pole strength is m/2 and dipole moment is p — Incorrect. With the pole strength halved and the length unchanged, the moment cannot stay \( p \).
Option (4) pole strength is m and dipole moment is p/2 — Incorrect. This is the result for a cut across the length (perpendicular to the axis): the cross-section, and so the pole strength, is unchanged while the length is halved.