91Ó°ÊÓ

In a magnetic field, a magnetic dipole (such as a needle) experiences a magnetic torque and a magnetic force. The torque tends to align the dipole with the magnetic field, and the force pushes or pulls the dipole. The torque and force experienced by the dipole depend on the field's uniformity.

The magnetic torque experienced by a magnetic needle in a magnetic field is given by the equation: \( \tau = \vec{m} \times \vec{B} \) where \(\vec{m}\) is the magnetic moment of the needle, and \(\vec{B}\) is the magnetic field. Since the needle is kept in a non-uniform magnetic field, the torque on the needle will be non-zero as the magnetic moment vector and the magnetic field vector will not be aligned in all regions.

The magnetic force experienced by a magnetic dipole in a non-uniform magnetic field is given by: \( \vec{F} = (\vec{m} \cdot \nabla) \vec{B} \) In a non-uniform magnetic field, the gradient of the field \(\nabla \vec{B}\) is non-zero. Since the magnetic moment vector \(\vec{m}\) is also non-zero, the magnetic needle will experience a non-zero magnetic force.

Based on our analysis of magnetic torque and force on the needle, we can now determine the correct answer to the exercise: (A) a torque but not a force - Incorrect, as we have shown that the needle experiences both torque and force in a non-uniform magnetic field. (B) neither a force nor a torque - Incorrect, as we have shown that the needle experiences both torque and force in a non-uniform magnetic field. (C) a force and a torque - Correct, as we have shown that the needle experiences both torque and force in a non-uniform magnetic field. (D) a force but not a torque - Incorrect, as we have shown that the needle experiences both torque and force in a non-uniform magnetic field. Hence, the correct option is (C) a force and a torque.