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Potential energy of a dipole
Intermediate
Lowest when aligned.
U = −p·EU = −p·E = −pE cosθ. It's lowest when aligned (θ = 0) and highest when opposite. Microwaves heat food by rotating water dipoles.
Work to rotate by 180°: 2pE.
Zero reference is at θ = 90°.
In more detail
The potential energy of a dipole in an electric field is U = −p·E. It is lowest when the dipole is aligned with the field and highest when it is anti-aligned.
Real-world uses
- Molecules align with applied fields, which is used in chemical analysis.
- Polar molecules are attracted to charged surfaces by dipole energies.
- Chemists explain why polar molecules line up in an electric field, which lowers their potential energy.
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Frequently asked questions
Why is the energy negative?
Because the dipole prefers alignment, so the energy is reduced when the angle is small.
Is the energy the same as torque?
No. Torque is the derivative of energy with respect to angle.
When is the dipole energy lowest?
When the dipole points along the field, because the potential energy is minus p dot E.
Related topics in Electrostatics
Electric dipole · Field of a dipole · Torque on a dipole in a field · Electric flux · Gauss's law · Field of infinite line charge