Question

The value of torque \( \boldsymbol{\tau} \) experienced by a current loop of magnetic moment \( \mathbf{m} \) placed in a magnetic field \( \mathbf{B} \) is:

• A. \( \boldsymbol{\tau} = \mathbf{m} \times \mathbf{B} \)
• B. \( 26 \)
• C. \( \boldsymbol{\tau} = \frac{B}{m} \)
• D. \( \boldsymbol{\tau} = \mathbf{B} \times \mathbf{m} \)

Hint:

Torque on magnetic dipole: \[ \boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}. \] Direction is perpendicular to both \( \mathbf{m} \) and \( \mathbf{B} \).

Answer 1

The Correct Option is A

The torque \( \boldsymbol{\tau} \) experienced by a magnetic dipole moment \( \mathbf{m} \) placed in a magnetic field \( \mathbf{B} \) is given by the vector cross product: \[ \boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}. \] This torque arises because the magnetic dipole tends to align itself with the external magnetic field. The magnitude of the torque is: \[ |\boldsymbol{\tau}| = m B \sin \theta, \] where \( \theta \) is the angle between the magnetic moment \( \mathbf{m} \) and the magnetic field \( \mathbf{B} \). The direction of the torque is perpendicular to the plane formed by \( \mathbf{m} \) and \( \mathbf{B} \), following the right-hand rule. Physically, this torque causes the magnetic dipole to rotate, reducing the angle \( \theta \) until \( \mathbf{m} \) aligns parallel to \( \mathbf{B} \), minimizing the potential energy of the system.