Electric Dipole Moment Calculator
A pair of equal and opposite charges ±q separated by a distance d forms an electric dipole with moment p = q·d, pointing from the negative to the positive charge. Enter any two of p, q and d and the third is solved. Add an external field to get torque and energy, and a distance to get the dipole's own field.
p = q · dτ = p · E · sin θU = −p · E · cos θStep-by-step solution
Companion quantities
Dipole in a field
The dipole points from −q to +q. The field exerts a torque that turns p toward E.
Dipole field versus distance
Reference data
| Molecule | Dipole (D) | Dipole (10⁻³⁰ C·m) |
|---|
| Angle θ | Torque τ (N·m) | Energy U (J) | U / kBT (298 K) |
|---|
| Unit | In C·m | In debye |
|---|---|---|
| 1 debye (D) | 3.33564 × 10⁻³⁰ | 1 |
| 1 e·Å | 1.60218 × 10⁻²⁹ | 4.8032 |
| 1 e·nm | 1.60218 × 10⁻²⁸ | 48.032 |
| 1 C·m | 1 | 2.99792 × 10²⁹ |
Molecular values vary slightly with the measurement method and state. Your dipole's row is highlighted in the molecule table when it is within 15%.
FAQ
What is a debye?
The debye (D) is the traditional unit for molecular dipole moments. One debye is about 3.336 × 10⁻³⁰ C·m, roughly the moment of an electron and a proton held 0.21 Å apart. Water's dipole is about 1.85 D.
Which way does the dipole point?
By physics convention the dipole moment vector points from the negative charge toward the positive charge. Chemists often draw the arrow the other way (from positive to negative), so check which convention a source uses.
Why do some molecules have zero dipole moment?
Symmetric molecules such as CO₂, CH₄ and H₂ have individual bond dipoles that cancel, so the net dipole is zero even though the bonds are polar. Shape matters as much as bond polarity.
How is the field of a dipole different from a point charge?
It falls off as 1/r³ instead of 1/r². Along the axis the field is 2kp/r³, and on the perpendicular bisector it is kp/r³, half as strong and pointing the opposite way. The formulas apply when r is much larger than d.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| p | Electric dipole moment | C·m |
| q | Magnitude of charge | C |
| d | Separation distance between charges | m |
What it means
The electric dipole moment p is a measure of the separation of positive and negative charges in a system. It is defined as p = q·d, where q is the magnitude of each charge and d is the displacement vector from negative to positive charge. The dipole moment is a vector quantity and is important in understanding the behaviour of molecules, dielectrics, and antennas. In an external electric field, a dipole experiences a torque that tends to align it with the field. Dipoles play a key role in the polarisation of dielectric materials, affecting the overall capacitance of a capacitor. In electromagnetism, the dipole field is the leading term in the multipole expansion. Example: For a pair of charges +1.6×10⁻¹⁹ C and −1.6×10⁻¹⁹ C separated by 0.1 nm (1×10⁻¹⁰ m), the dipole moment is p = 1.6e-19 * 1e-10 = 1.6×10⁻²⁹ C·m. This is typical of a polar molecule like water.
Worked example
Electric Dipole Moment – Practical Example
Real‑World| Parameter | Value |
|---|---|
| q | 2 µC = 2×10⁻⁶ C |
| d | 1 cm = 0.01 m |
| Formula | p = q·d |
Common mistakes
- Charge q and separation d: The dipole moment points from negative to positive charge.
- Units: C·m (coulomb‑metre).
- Vector: It is a vector quantity – direction matters.
- Torque: A dipole in an electric field experiences torque τ = p × E.
- Potential energy: U = −p·E for a dipole in a field.
Applications
The electric dipole moment p = q·d represents the separation of opposite charges, a vector pointing from negative to positive. This concept is vital for understanding the behaviour of polar molecules, dielectric polarisation, and the generation of electromagnetic radiation. Engineers use it in designing microwave antennas, studying material polarisation, and understanding the interaction of fields with matter. By calculating the dipole moment, they can predict the response of materials to electric fields and design devices such as phase shifters and modulators. This formula is fundamental in electromagnetics and materials science.
- Design of microwave and RF components (phase shifters, antennas)
- Understanding dielectric polarisation and permittivity
- Molecular and chemical analysis via dipole moments
- Electromagnetic field interaction with materials
- Educational foundation of dipole radiation
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