When a dipole moment p aligns with a uniform external electric field E, what happens to the dipole's potential energy?

When a dipole moment p aligns with a uniform external electric field E, what happens to the dipole's potential energy?

• A. The energy decreases; U = − p · E; minimum when θ = 0
• B. The energy increases; U = p · E; maximum when θ = 0
• C. The energy remains unchanged
• D. The energy becomes zero

Answer: (A)

The potential energy of a dipole in a uniform electric field depends on how the dipole moment p is oriented relative to the field E. It follows U = - p · E, or U = - p E cos θ, where θ is the angle between p and E. The negative sign means the system lowers its energy when p points in the same direction as E. When the dipole is aligned with the field (θ = 0), cos θ = 1, so U = - p E. This is the smallest (most negative) energy the system can have for any nonzero p and E, so the energy decreases as the dipole aligns with the field. If the dipole were opposite to the field (θ = 180°), the energy would be + p E (a maximum). If it were perpendicular (θ = 90°), the energy would be zero.

The potential energy of a dipole in a uniform electric field depends on how the dipole moment p is oriented relative to the field E. It follows U = - p · E, or U = - p E cos θ, where θ is the angle between p and E. The negative sign means the system lowers its energy when p points in the same direction as E.

When the dipole is aligned with the field (θ = 0), cos θ = 1, so U = - p E. This is the smallest (most negative) energy the system can have for any nonzero p and E, so the energy decreases as the dipole aligns with the field. If the dipole were opposite to the field (θ = 180°), the energy would be + p E (a maximum). If it were perpendicular (θ = 90°), the energy would be zero.