In nonpolar solvents, surfactants stabilize charge through the formation of reverse micelles; this enables the dissociation of charge from the surfaces of particles, thereby charge-stabilizing particle suspensions. We investigate the dynamics of such charged particles by directly visualizing their motion across a microfluidic channel in response to an external electric field. The presence of the reverse micelles has a significant effect on particle motion: in a constant field, the particles initially move, then slow down exponentially, and eventually stop. This is due to the accumulation of reverse micelles at the channel walls, which screens the applied field, leading to the subsequent decay of the internal electric field. The time constant of decay depends on the electrical conductivity of the particle suspension and the width of the channel; this behavior is modeled as an equivalent RC circuit.