Dynamic image forces near a metal surface and the point-charge motion

Abstract

The problem of charge motion governed by image force attraction near a plane metal surface is considered and solved self-consistently. The temporal dispersion of metal dielectric permittivity makes the image forces dynamic and, hence, finite, contrary to the results of the conventional approach. Therefore, the maximal attainable velocity turns out to be also finite and comprises a small portion of light velocity so that there is no need for any relativistic generalization of the problem. The time needed for an electron to achieve the surface from the initial position is calculated. The solution of the problem presented may enable undergraduates and lecturers to perceive the limitations of conventional electrostatics when applied to the surface science of real materials.