  The electrostatic potential in a superconductor is studied. To this end
Bardeen's extension of the Ginzburg-Landau theory to low temperatures is used
to derive three Ginzburg-Landau equations - the Maxwell equation for the vector
potential, the Schroedinger equation for the wave function and the Poisson
equation for the electrostatic potential. The electrostatic and the
thermodynamic potential compensate each other to a great extent resulting into
an effective potential acting on the superconducting condensate. For the
Abrikosov vortex lattice in Niobium, numerical solutions are presented and the
different contributions to the electrostatic potential and the related charge
distribution are discussed.
