This paper uses a tight-binding scattering formalism to calculate the spati
al distribution of the electric current and field in small phase-coherent c
onductors. The calculation is simple and efficient, allowing one to obtain:
simultaneous pictures of the current density and the local potential and f
ield in a wide range of atomic-scale structures. The use of the method is i
llustrated by two examples. The first shows the formation of a resistivity
dipole across an extended obstacle. The second is conduction through a doub
le: constriction, where we compare the current and potential distributions
at and off resonance. The current pattern at resonance is related to the wa
vefunction of the quasibound state responsible for the resonance. Off reson
ance, large internal closed currents are found inside the double constricti
on. At resonance the potential drops are concentrated at the entrances to t
he constriction, while off resonance essentially all of the potential drop
occurs in the interior of the double constriction.