  The existence of gauge conditions involving second-order derivatives of
potentials is not well known in classical electrodynamics. We introduce one of
these gauges, the Coulomb static gauge, in which the scalar potential is given
by the Coulomb static potential. We obtain an explicit expression for the
associated vector potential and show how the scalar and vector potentials in
this gauge yield the retarded electric and magnetic fields. We note the close
relation between the proposed gauge and the temporal gauge.
