What it does
An electric dipole is a pair of equal and opposite charges, +q and −q, a small distance d apart. Its dipole moment p = q d points from the negative charge to the positive one. Molecules such as water behave like tiny dipoles.
Put a dipole in a uniform electric field and the + end is pushed along the field while the − end is pushed the other way. The two forces are the same size, so the dipole does not move along, but they turn it: the torque is τ = pE sin θ, where θ is the angle between p and E. The torque always turns p towards the field. The potential energy is U = −pE cos θ: lowest when p lines up with E, highest when it points against it.
This page draws the dipole in a field, the two forces and the turning arrow, and works out p, τ, U and the work needed to turn it, as you change the angle, the charges, the separation and the field. A graph shows τ and U for every angle with a dot at yours. Press Let it go and the dipole swings about the field direction like a pendulum, slowing down a little each swing.
It follows the electric charges and fields chapter of Class 12 Physics (electric dipole, dipole in a uniform external field), and the potential energy of a dipole in the next chapter. Work out the forces between single charges first in coulomb forces, see the curved field of a free dipole in the field lines, and see why molecules have dipole moments in dipole polarity.
How to use it
- Drag the dipole round with your finger or mouse, or use the angle slider (0° to 180°).
- Set the charges (1 to 10 µC), the separation (1 to 5 cm) and the field (1 × 10⁴ to 1 × 10⁵ N/C).
- Read τ and U, the working, and the facts: the moment, the force on each charge, the largest torque, and the work to turn the dipole from 0°.
- Press Let it go to release it, and Stop to hold it. The swing is slowed down so you can follow it.
Worked example
The page opens with ±2 µC charges 2 cm apart, in a field of 5 × 10⁴ N/C, at θ = 30°.
- p = q d = 2 × 10⁻⁶ × 0.02 = 4 × 10⁻⁸ C m.
- τ = p E sin θ = 4 × 10⁻⁸ × 5 × 10⁴ × sin 30° = 0.001 N m.
- U = −p E cos θ = −4 × 10⁻⁸ × 5 × 10⁴ × 0.866 = −0.00173 J.
- Each charge feels qE = 2 × 10⁻⁶ × 5 × 10⁴ = 0.1 N, in opposite directions.
- Turning it from 0° to 30° takes W = pE (1 − cos 30°) = 2.68 × 10⁻⁴ J.
Tips
- θ = 0° is a stable balance (it comes back if nudged); θ = 180° is unstable (it tips over).
- The torque is the slope of the energy graph with its sign changed: τ = −dU/dθ. Where U is steepest, τ is largest.
- In a field that is not uniform, the two forces are not quite equal, so the dipole is also pulled along. This page keeps the field uniform.
FAQ
Why is U zero at 90°? Only differences in energy matter, so we may choose where U = 0. The usual choice, which gives U = −pE cos θ, puts it at 90°.
Is the swing speed real? No. The page slows the swing down so you can see it; how fast a real dipole swings depends on its mass.
Is anything saved? No. Everything is worked out on this page and nothing leaves your device.
Where the numbers come from
- Electric dipole in a uniform field: p = qd, τ = p × E (size pE sin θ), U = −p·E = −pE cos θ, work W = pE (cos θ₁ − cos θ₂). Standard physics results.
- Checked against an independent Python script, and the torque checked as −dU/dθ by a numerical derivative.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.