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On the velocity-dependence of image forces

Classical theory yields an exact expression for the Lorentz force f(ζ, u) on a point charge Q which has third coordinate ζ, and which has always moved with strictly constant velocity u in a halfspace bounded by a perfectly reflecting xy plane. On its own, f would produce an acceleration directed towards the surface, smaller for any nonzero than for vanishing u. It is compared, to orders u2/c2 and Q2, with quantum-perturbative predictions for an otherwise free particle near variously modelled imperfect reflectors. For large ζ and/or high reflectivity, the quantum results are dominated by components free of ℏ, and we reason that such components should agree with the corresponding classical perfect-reflector results. This test is applied to several theories: some pass and some fail.