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