  It is generally accepted that vortex core is charged, what illustrates that
even in stationary superconductors electric field may be present. Vortex
structure and other properties of superconductors are usually calculated in the
framework of the Ginzburg-Landau theory, which does not cover electric field.
We show that the generalization of the GL theory due to Bardeen allows one to
derive a third GL equation for the electrostatic potential. Since the Bardeen
theory applies to all temperatures, the presented theory enables one to
calculate charge profiles of the vortex under quite general conditions. The
theory is consistent with the BCS-Gorkov results.
