Analyses of the effect of radial electric field distribution on the steady flow of an ideal electro-rheological fluid in a rotating clutch and pressure-driven valve with a potential difference between the cylindrical electrodes are presented. The continuum model is a Bingham plastic in which the viscosity is constant and the yield stress depends upon the magnitude of the electric field, E, and is proportional to E - E-0, where E-0 is a constant threshold below which little yield stress is generated. The electric field distribution is assumed to be that of an ideal dielectric, the field being unaffected by the now. Flow patterns are presented for different ranges of applied voltage and compared with corresponding results for materials for which tau(e) is proportional to E-2.