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An electric dipole moves with velocity v in a uniform magnetic field B directed into the plane of the paper. In Case-I the dipole moment vector p is parallel to v (p along v), and in Case-II the dipole moment vector p is perpendicular to v. Which of the following is correct?
- The dipole experiences a net force in Case-I due to the external magnetic field
- The dipole experiences a net force in Case-II due to the external magnetic field
- The dipole experiences a net torque in Case-I due to the external magnetic field
- The dipole experiences a net torque in Case-II due to the external magnetic field
Correct answer: The dipole experiences a net torque in Case-II due to the external magnetic field
Solution
An electric dipole consists of charges +q and -q separated by a small distance 2l. Both charges move with the same velocity v in the uniform magnetic field B. The magnetic force on +q is F1 = q(v cross B) and on -q is F2 = -q(v cross B) = -F1. Since F1 and F2 are equal and opposite, the NET FORCE on the dipole is always zero in a uniform magnetic field regardless of orientation — so neither Case-I nor Case-II has a net translational force. For torque: if p is parallel to v (Case-I), both force vectors on +q and -q are along the same line perpendicular to v and along the dipole axis direction — they produce no net torque. If p is perpendicular to v (Case-II), the forces on +q and -q are antiparallel but displaced, forming a couple that produces a net torque. Hence a net torque acts on the dipole in Case-II only.
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