Talman [Phys. Rev. Lett. 56, 1429 (1986)] has proposed a novel relativistic effect that occurs when a charged particle beam is bent in the magnetic field from an external dipole. The consequence of this effect is that the space-charge forces from the particles do not exhibit the usual inverse-square energy dependence and some part of them are, in fact, independent of energy. This led to speculation that this effect could introduce significant emittance growth for a bending electron beam. Subsequently, it was shown that this effect’s influence on the beam’s transverse motion is canceled for a dc beam by a potential depression within the beam (to first order in the beam radius divided by the bend radius). In this paper, we extend the analysis to include short bunch lengths (as compared to the beam pipe dimensions) and find that there is no longer the cancellation for forces both transverse to and in the direction of motion. We provide an estimate for the emittance growth as a function of bend angle, beam radius, and current, and for magnetic compression of an electron bunch.