What is the torque on a dipole in a uniform external field?

What is the torque on a dipole in a uniform external field?

• A. τ = p × E; magnitude τ = p E sin θ
• B. τ = E × p
• C. τ = p × E; magnitude τ = p^2 E
• D. τ = p / E

Answer: (B)

The torque on an electric dipole in a uniform external field is given by the cross product of the dipole moment and the field: τ = p × E. Here p points from the negative to the positive charge, E is the external field, and the magnitude is τ = p E sin θ, where θ is the angle between p and E. The direction of τ is perpendicular to the plane formed by p and E, determined by the right-hand rule, and this torque tends to rotate the dipole so that p aligns with E. If you reverse the order in the cross product (E × p), you’d get the same magnitude but the opposite direction, which is not the actual torque. Forms like p^2 E or p/E don’t have the right dependence on angle or units.

The torque on an electric dipole in a uniform external field is given by the cross product of the dipole moment and the field: τ = p × E. Here p points from the negative to the positive charge, E is the external field, and the magnitude is τ = p E sin θ, where θ is the angle between p and E. The direction of τ is perpendicular to the plane formed by p and E, determined by the right-hand rule, and this torque tends to rotate the dipole so that p aligns with E. If you reverse the order in the cross product (E × p), you’d get the same magnitude but the opposite direction, which is not the actual torque. Forms like p^2 E or p/E don’t have the right dependence on angle or units.