If M is magnetic moment and B is magnetic field, then the torque is g…

The correct answer is Option (2) → \( \vec{M}\times\vec{B} \)

A magnetic dipole in a uniform field feels a torque that tends to turn it into line with the field. Its magnitude is \( MB\sin\theta \), and as a vector it is the cross product of the moment and the field, taken in that order.

    \( \displaystyle \vec{\tau} = \vec{M}\times\vec{B} \)

Option (1) \( \vec{M}\cdot\vec{B} \) — Incorrect. The dot product is a scalar; \( -\vec{M}\cdot\vec{B} \) is the potential energy of the dipole, not the torque.

Option (2) \( \vec{M}\times\vec{B} \) — Correct. \( \vec{\tau} = \vec{M}\times\vec{B} \), of magnitude \( MB\sin\theta \).

Option (3) \( \vec{B}\times\vec{M} \) — Incorrect. \( \vec{B}\times\vec{M} = -\vec{M}\times\vec{B} \), so it has the right magnitude but the opposite direction.

Option (4) \( \displaystyle\frac{|\vec{M}|}{|\vec{B}|} \) — Incorrect. The ratio \( M/B \) does not have the units of torque and does not depend on the angle.

Note: A similar question was also asked in CUET (UG) 2025 on 29-05-2025 (Slot 1).

NCERT (2026-27):
Torque on Current Loop, Magnetic Dipole – “… The torques in Eqs. (4.20) and (4.21) can be expressed as vector product of the magnetic moment of the coil and the magnetic field. … Then as the angle between m and B is θ, Eqs. (4.20) and (4.21) can be expressed by one expression

    \( \displaystyle \boldsymbol{\tau} = \mathbf{m} \times \mathbf{B} \qquad (4.23) \)”