A rectangular loop carries a steady current in a uniform magnetic field. The torque on the loop is largest when the field lies in the plane of the loop. When the plane of the loop makes an angle with the field, the torque is smaller. In the derivation of the torque, this is because
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → the perpendicular distance between the two forces of the couple becomes smaller
In a uniform field the forces on two opposite arms of the loop are equal, opposite and not along the same line. They form a couple, and the torque equals one force times the perpendicular distance between the two forces.
Option (1) the two forces that form the couple become smaller in size — Incorrect. Each of these forces is \( IbB \), where \( b \) is the length of the arm. The arm stays perpendicular to the field as the loop turns, so the size of the force does not change.
Option (2) the forces on the other two arms give a torque in the opposite sense — Incorrect. The forces on the other two arms are equal, opposite and act along the same line, the axis of the coil. They give neither a net force nor a torque.
Option (3) a net force now acts on the loop and reduces the torque — Incorrect. All the forces on the loop add up to zero in every position. A loop in a uniform field never feels a net force.
Option (4) the perpendicular distance between the two forces of the couple becomes smaller — Correct. When the normal to the loop makes an angle \( \theta \) with the field, the two forces come closer to the same line. The perpendicular distance between them becomes \( a\sin\theta \), so the torque becomes \( IAB\sin\theta \). This is less than \( IAB \), the value when the field lies in the plane of the loop.
NCERT (2026-27):
Torque on a rectangular current loop in a uniform magnetic field – “But they are not collinear! This results in a couple as before. The torque is, however, less than the earlier case when plane of loop was along the magnetic field. This is because the perpendicular distance between the forces of the couple has decreased.”