A small magnetised needle is placed in a uniform magnetic field. Its…

The correct answer is Option (1) → a torque but no net force

A magnetised needle behaves as a magnetic dipole. Its magnetic moment \( m \) is a vector that points from its south end to its north end. A uniform field has the same strength and direction at every point. In such a field the net force on a dipole is zero. The field still tries to turn the dipole along itself. This turning effect is the torque \( \tau = mB\sin\theta \).

Here \( \theta = 30^\circ \), so \( \sin\theta = \frac{1}{2} \) and the torque is not zero.

Option (1) a torque but no net force — Correct. The field is uniform, so no net force acts. The angle is not zero, so a torque turns the needle towards the field.

Option (2) a net force but no torque — Incorrect. A uniform field gives no net force on a dipole. The torque would be zero only if the needle lay along the field.

Option (3) both a net force and a torque — Incorrect. This happens in a non-uniform field. An iron nail near a bar magnet is an example. Here the field is uniform, so there is no net force.

Option (4) neither a net force nor a torque — Incorrect. The torque \( mB\sin\theta \) becomes zero only when \( \theta = 0^\circ \) or \( 180^\circ \). At \( 30^\circ \) a torque acts.

NCERT (2026-27):
Example 5.1 – “(b) A magnetised needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet, however, experiences a force of attraction in addition to a torque. …”

5.2.3 The dipole in a uniform magnetic field – “The torque on the needle is … In magnitude \( \tau = mB\sin\theta \) Here \( \tau \) is restoring torque and \( \theta \) is the angle between m and B.”