Electric dipole moment
A water molecule. A molecule of water is po-
lar because of the unequal sharing of its elec-
trons 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).
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 sys-
tem’s overall polarity.
In the simple case of two point charges,
one with charge + q and one with charge −
q, 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 vec-
tor 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 separ-
ated, but with a finite p = q d.
More generally, for a continuous distribu-
tion of charge confined to a volume V, the
corresponding expression for the dipole mo-
ment 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 refer-
ence point to the charge qi. Substitution into
the above integration formula provides:
This expression is equivalent to the previous
expression in the case of charge neutrality
and N = 2. For two opposite charges, denot-
ing 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 dir-
ected from the negative charge to the posit-
ive charge because the position vector of a
point is directed outward from the origin to
that point.
The dipole moment is most easily under-
stood when the system has an overall neutral
charge;