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An electric dipole moves with velocity v in a uniform magnetic field B directed into the plane of the paper. Consider two cases: Case I — the dipole moment p is parallel to v; Case II — the dipole moment p is perpendicular to v. Which of the following statements 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 I due to the external magnetic field.
Solution
Net force on dipole = +q(v x B) + (-q)(v x B) = 0 in all cases (uniform field). For torque: τ = p x (v x B) where p is the dipole moment vector. Let v = v x_hat, B = -B z_hat (into page), so v x B = vB y_hat. Case I: p || v means p = p x_hat. τ = (p x_hat) x (vB y_hat) = pvB (x_hat x y_hat) = pvB z_hat ≠ 0. Net torque exists in Case I. Case II: p perpendicular to v means p = p y_hat. τ = (p y_hat) x (vB y_hat) = pvB (y_hat x y_hat) = 0. No torque in Case II.
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