  Consideration of the balance of forces on superconducting condensate at low
frequencies leads to the well-known Josephson Relation. Using the
Ginzburg-Landau expression for the current, an expression relating the electric
field to the vortex velocity via the magnetic field is obtained. This result is
the Josephson Relation, supplemented by a term accounting for the inertia of
charge carriers. This Inertial Josephson Relation may be used at all
frequencies and may be viewed as the Josephson Relation extended to the case of
sub-gap high-frequency response. When applied to vortex dynamics it yields the
same conductivity as solution of the Ginzburg-Landau theory.
