Discussion
A magnetic dipole of dipole moment (\(\vec{m}\)) is placed in a non-uniform magnetic field \(\vec{B}\). If the position vector of the dipole is \(\vec{r}\) , the torque acting on the dipole about the origin is :
Answer: B
The torque is \(\vec{m} \times \vec{B} + \vec{r} \times \vec{\nabla}(\vec{m} \cdot \vec{B})\).
In a non-uniform field the dipole feels two things: a torque about its own centre, \(\vec{m} \times \vec{B}\), and a net force \(\vec{F} = \vec{\nabla}(\vec{m} \cdot \vec{B})\). About the origin, that force adds a moment \(\vec{r} \times \vec{F}\). The total torque about the origin is the sum.
\(\vec{m} \times \vec{B}\) alone is the torque in a uniform field or about the dipole's own centre. \(\vec{r} \times \vec{\nabla}(\vec{m} \cdot \vec{B})\) alone omits the intrinsic torque, and \(\vec{r} \times (\vec{m} \times \vec{B})\) has no physical meaning as a torque here.
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