How does an external electric field interact with a dipole?

When an electric dipole is placed in an external uniform electric field (E), it experiences a torque, but no net force.

1. Forces on the Dipole:
   • The positive charge (+q) experiences a force (F₊ = qE) in the direction of the electric field.
   • The negative charge (-q) experiences a force (F_- = -qE) of equal magnitude but in the opposite direction of the field.
2. Net Force:
   • Since these two forces are equal and opposite, they cancel each other out.
   • ΣF = F₊ + F_- = qE + (-qE) = 0
   • Therefore, the net force on a dipole in a uniform electric field is zero. This means the dipole's center of mass will not accelerate.
3. Torque on the Dipole:
   • Although the net force is zero, the two forces act at different points, creating a "couple" or turning force. This is called a torque (symbol τ).
   • This torque tries to rotate the dipole to align it with the electric field. The dipole is in its most stable, lowest-energy state when its dipole moment vector (p) is parallel to the electric field vector (E).
   • Formula: The magnitude of the torque is τ = pE sin(θ), where θ is the angle between p and E.
   • The torque is maximum when the dipole is perpendicular to the field (θ = 90°) and zero when it is aligned (θ = 0°).

(Note: In a non-uniform electric field, the forces F₊ and F_- would have different magnitudes, resulting in both a net torque and a net force on the dipole.)