Quantities defining the electric dipole moment of two point charges.
Animation showing the electric field
of an electric dipole. The dipole consists of two point electric charges of opposite polarity located close together. A transformation from a point-shaped dipole to a finite-size electric dipole is shown.
A molecule of water
is polar because of the unequal sharing of its electrons in a "bent" structure. A separation of charge is present with negative charge in the middle (red shade), and positive charge at the ends (blue shade).
Often in physics the dimensions of a massive object can be ignored and can be treated as a pointlike object, i.e. a point particle. Point particles with electric charge are referred to as point charges. Two point charges, one with charge +q and the other one with charge −q separated by a distance d, constitute an electric dipole (a special case of an electric multipole). For this case, the electric dipole moment has a magnitude
and is directed from the negative charge to the positive one. Some authors may split d in half and use s = d/2 since this quantity is the distance between either charge and the center of the dipole, leading to a factor of two in the definition.
A stronger mathematical definition is to use vector algebra, since a quantity with magnitude and direction, like the dipole moment of two point charges, can be expressed in vector form
where d is the displacement vector pointing from the negative charge to the positive charge. The electric dipole moment vector p also points from the negative charge to the positive charge.
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.
This quantity is used in the definition of polarization density.