The use of finite size conductance electrode strips for the identification of dispersed phase flows may lead to difficulties related to the failure of homogeneous theories for the effective conductivity of dispersions in the particular geometry. In this context, a model problem is presented here: circular nonconducting entities dispersed in a conducting liquid flow at constant velocity over a nonconducting wall with strip electrodes flush mounted on it. The mathematical model is formulated in detail and is decomposed to electrostatic and to swarm generation subproblems. The electrostatic problem is simplified for dilute swarm of small, compared to the electrode width, entities for which an approximate analytical closed form solution is derived. A stochastic algorithm is developed for the generation of entity swarms. It is shown that a swarm generates fluctuations to the effective conductance measured by the electrodes. The strength of the fluctuations is related to the variations of the local electric current magnitude of the electrical field undisturbed by the entities at a distance equal to the average distance between entities. The present work is a first step to understand the interaction between entity swarms flowing over strip electrodes in order to explore the possibility of exploiting the fluctuating conductance signal for the characterization of the swarm further to a simple volume fraction determination.