Electric Dipole Moment & Field Calculator

Inputs

Charge magnitude q (C) Use positive magnitude; the model uses ±q internally.

Separation s (m) Center-to-center distance between +q and −q.

Dipole orientation (û)

Model

Field point x (m)

Field point y (m)

Field point z (m)

Permittivity ϵ0 (F/m) Vacuum: 8.8541878128×10⁻¹². For materials, use ϵ = ϵr×ϵ0.

Output decimals

Results

Enter values and press Calculate to see moment, field, and potential.

Equations

p = q · s · û

Point-dipole:
E(r) = (1/(4πϵ0)) [ 3(p·r) r / r^5 − p / r^3 ]
V(r) = (1/(4πϵ0)) (p·r) / r^3

Exact two-charge (±q at ±aû, where a = s/2):
E = k q [ (r − aû)/|r − aû|^3 − (r + aû)/|r + aû|^3 ]
V = k q [ 1/|r − aû| − 1/|r + aû| ]

Frequently Asked Questions

1) What is the electric dipole moment?

It quantifies a separated pair of opposite charges: p = q·s·û. The SI unit is coulomb–meter (C·m). Larger magnitudes indicate stronger polarity.

2) Which orientation should I choose?

Pick the axis along which the positive charge lies at +s/2 and the negative charge at −s/2. The moment vector points in the +û direction.

3) Point‑dipole vs exact model — what’s the difference?

The point‑dipole model assumes the observation point is far from the dipole (|r| ≫ s), collapsing the pair into a single moment p. The exact model resolves both charges and is accurate everywhere except at the singularities.

4) When is the point‑dipole approximation valid?

As a rule of thumb, when |r| is at least ~5–10 times larger than s. The calculator warns you if the chosen geometry falls outside that range.

5) Why do fields “blow up” near the charges?

Ideal point charges have 1/r² fields and infinite values at r = 0. Real systems have finite size; the model ceases to apply at sufficiently small distances.

6) How do I model materials?

Use ϵ = ϵ_r·ϵ₀, where ϵ_r is the relative permittivity of the medium. Set that value in the ϵ₀ field as needed (e.g., water has ϵ_r ≈ 80 at room temperature).

7) What units do results use?

Inputs use SI (C, m, F/m). The moment is in C·m, the field in V/m (equivalently N/C), and the scalar potential in volts.