  We study the steady state response of a dilute monovalent electrolyte
solution to an external source with a constant relative velocity with respect
to the fluid. The source is taken as a combination of three perturbations: an
external force acting on the fluid, an externally imposed ionic chemical
potential, and an external charge density. The linear response functions are
obtained analytically and can be decoupled into three independent terms,
corresponding to (i) fluid flow and pressure, (ii) total ionic number density
and current, and (iii) charge density, electrostatic potential and electric
current. It is shown how the uniform flow breaks the equilibrium radial
symmetry of the response functions, leading to a distortion of the ionic cloud
and electrostatic potential, which deviate from the standard Debye-H\"uckel
result. The potential of a moving charge is under-screened in its direction of
motion and over-screened in the opposite direction and normal plane. As a
result, an unscreened dipolar electric field and electric currents are induced
far from the charged source. We relate our general formalism to several
experimental setups, such as colloidal sedimentation.
