An integral transport theory for determining the distribution function of test particles, which diffuse in the presence of an external conservative force in a system of field particles, is proposed. How—for the case in which the test particles are taken to be electrons—the validity of Ohm’s law can be checked and the subsequent evaluation of electrical conductivity can be carried out is illustrated for different models of energy exchange between the test and the field particles under consideration and for different geometries of the external source. Removal effects of test particles are accounted for throughout the discussion.