A bar magnet and its equivalent solenoid produce the same magnetic field. How do their magnetic moments compare?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both are the same.
Far from its ends, the field of a bar magnet or of a solenoid depends only on its magnetic moment. On the axis, it is \( B=\mu_0\,2m/4\pi r^{3} \) for both.
Option (1) The magnetic moment of the solenoid is higher. — Incorrect. A larger moment would give the solenoid a stronger field at the same distance, but the two fields are the same.
Option (2) The magnetic moment of the bar magnet is higher. — Incorrect. If the bar magnet had the larger moment, its field would be stronger at the same distance. But the two fields are the same.
Option (3) Both are the same. — Correct. The equivalent solenoid is the one that produces the same magnetic field as the bar magnet. This field depends on the magnetic moment, so the two moments are equal.
Option (4) It cannot be predicted. — Incorrect. The field fixes the moment through \( B=\mu_0\,2m/4\pi r^{3} \). So equal fields at the same distance give equal moments, and the answer is definite.
NCERT (2026-27):
Bar Magnet as an Equivalent Solenoid – “… The magnetic moment of a bar magnet is thus equal to the magnetic moment of an equivalent solenoid that produces the same magnetic field.”