Surfactant molecules in a non-polar liquid form charged and uncharged inverse micelles. When a potential difference is applied over the mixture, the charged inverse micelles drift towards the electrode with the opposite polarity. The motion of charges is associated with a transient current, which can be measured in an external circuit. In this paper, transient currents and steady state charge densities are described analytically in different ranges of parameter values (applied voltage, charge density, device thickness, mobility,...). The generation of additional charged inverse micelles and the electrophoretic motion of colloidal particles in the mixture is modelled and measured experimentally.