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In physics, the electric dipole moment is a measure of the separation of positive and negative electrical charges in a system of charges, that is, a measure of the charge system's overall polarity.
In the simple case of two point charges, one with charge and one with charge , the electric dipole moment p is:
where d is the displacement vector pointing from the negative charge to the positive charge. Thus, the electric dipole moment vector p points from the negative charge to the positive charge. There is no inconsistency here, because the electric dipole moment has to do with the positions of the charges, not the field lines.
An idealization of this two-charge system is the electrical point dipole consisting of two (infinite) charges only infinitesimally separated, but with a finite p = q d.
More generally, for a continuous distribution of charge confined to a volume V, the corresponding expression for the dipole moment is:
where r locates the point of observation and d3r0 denotes an elementary volume in V. For an array of point charges, the charge density becomes a sum of Dirac delta functions:
where each is a vector from some reference point to the charge . Substitution into the above integration formula provides:
This expression is equivalent to the previous expression in the case of charge neutrality and . For two opposite charges, denoting the location of the positive charge of the pair as and the location of the negative charge as :
showing that the dipole moment vector is directed from the negative charge to the positive charge because the position vector of a point is directed outward from the origin to that point.
The dipole moment is most easily understood when the system has an overall neutral charge; for example, a pair of opposite charges, or a neutral conductor in a uniform electric field. For a system of charges with no net charge, the relation for electric dipole moment is:
which is the vector sum of the individual dipole moments of the neutral charge pairs. (Because of overall charge neutrality, the dipole moment is independent of the observer's position r.) Thus, the value of p is independent of the choice of reference point, provided the overall charge of the system is zero.
When discussing the dipole moment of a non-neutral system, such as the dipole moment of the proton, a dependence on the choice of reference point arises. In such cases it is conventional to choose the reference point to be the center of mass of the system or the center of charge, not some arbitrary origin.[1] This convention ensures that the dipole moment is an intrinsic property of the system.