  It is shown that conserved charges associated with a specific subclass of
gauge symmetries of Maxwell electrodynamics are proportional to the well known
electric multipole moments. The symmetries are residual gauge transformations
surviving after fixing the Lorenz gauge, and have nontrivial charge. These
"Multipole charges" receive contributions both from the charged matter and
electromagnetic fields. The former is nothing but the electric multipole moment
of the source. In a stationary configuration, there is a novel equipartition
relation between the two contributions. The multipole charge, while conserved,
can freely interpolate between the source and the electromagnetic field, and
therefore can be propagated with the radiation. Using the multipole charge
conservation, we obtain infinite number of constraints over the radiation
produced by the dynamics of charged matter.
