The rf particle separator, proposed in 1959 by W.K.H. Panofsky and now in preparation for the Brookhaven Alternating Gradient Synchrotron, required a rf structure which gives a transverse impulse to a passing relativistic particle. In order to produce an accumulative transverse deflection of a traveling charged particle with an electromagnetic field, it is necessary that the field contains a synchronous component and in principle, waveguides and cavities are equivalent with respect to the particle dynamics. It was pointed out by H.G. Hereward, that the electric and magnetic deflection of a transverse electric mode (i.e., with no electric field component parallel to the direction of the particle velocity) cancel exactly at all particle velocities. The deflecting force of a transverse magnetic mode on a synchronous particle with the velocity v is proportional to the factor 1-(v/c)2 and vanishes therefore in the case of relativistic particles.