Two wires of equal lengths carrying equal currents bent in the form of two loops, one in square shape and the other in circular shape having one turn only are suspended in same, uniform magnetic field perpendicular to the plane of loops.
Choose the correct option
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → both the loops experience zero torque
The torque on a current loop in a uniform field depends on the angle between its magnetic moment and the field. The magnetic moment \( \vec{m} = I\vec{A} \) is perpendicular to the plane of the loop.
\( \tau = mB\sin\theta = IAB\sin\theta \)
The field is perpendicular to the plane of each loop, so it is parallel to \( \vec{m} \) and \( \theta = 0^\circ \):
\( \tau = IAB\sin 0^\circ = 0 \)
This holds whatever the area, so both loops experience zero torque, even though the circle encloses more area than the square.
NCERT (2026-27):
Torque on Current Loop, Magnetic Dipole – “… Then as the angle between \( \mathbf{m} \) and \( \mathbf{B} \) is \( \theta \), Eqs. (4.20) and (4.21) can be expressed by one expression
\( \displaystyle \boldsymbol{\tau} = \mathbf{m} \times \mathbf{B} \qquad (4.23) \)”
Torque on Current Loop, Magnetic Dipole – “… From Eq. (4.23), we see that the torque \( \tau \) vanishes when \( \mathbf{m} \) is either parallel or antiparallel to the magnetic field \( \mathbf{B} \).”