Optics, electromagnetic theory Definition

Electric dipole moment

Definition

Fix an origin in $\R^3$ . For a system of point charges $q_1, \dots, q_n$ at points $x_1, \dots, x_n \in \R^3$ , the electric dipole moment is the vector $p = \sum_{i=1}^{n} q_i \, x_i.$ For an integrable charge density $\rho \colon \R^3 \to \R$ with $\int \abs{y} \abs{\rho(y)} \, dy < \infty$ , the electric dipole moment is $p = \int_{\R^3} y \, \rho(y) \, dy.$

Remarks

If the origin moves to $a$ , the moment becomes $p - Q a$ , where $Q$ is the total charge. So $p$ does not depend on the origin exactly when $Q = 0$ . Example: charges $+q$ at $(0,0,d/2)$ and $-q$ at $(0,0,-d/2)$ give $p = (0, 0, qd)$ , for any choice of origin, since $Q = 0$ . Non-example: a single charge $q \ne 0$ has no intrinsic dipole moment, since its moment $q x_1$ changes with the origin and vanishes when the origin is at $x_1$ . A dipole of moment $p$ in a uniform field $E$ feels the torque $p \times E$ and has potential energy $-p \cdot E$ . The SI unit is the coulomb metre.

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Electric charge concept
Electric dipole moment definition

Tag	`HFH9QNMYKG`
URI	`m2://HFH9QNMYKG`
Kind	definition
Writing	W0 stub
MSC	78A30
Defines	Electric dipole moment
Uses	Electric charge
Changed	3 November 2026

Electric dipole moment

Definition

Remarks

Reading path

Further reading

What this page needs for W1

What links here