Electrodynamic friction of a charged particle passing a conducting plate

TL;DR

This paper investigates the electromagnetic friction experienced by a charged particle moving near a conducting surface, revealing distinct behaviors of electric and magnetic contributions across velocity regimes and linking to Cerenkov radiation.

Contribution

It provides a detailed analysis of the classical electromagnetic friction using the Drude model, highlighting the magnetic contribution's maximum and its persistence at high velocities.

Findings

Magnetic friction contribution peaks below the speed of light.

Friction persists at zero resistivity at high velocities.

The formalism also describes Vavilov-Cerenkov radiation.

Abstract

The classical electromagnetic friction of a charged particle moving with prescribed constant velocity parallel to a planar imperfectly conducting surface is reinvestigated. As a concrete example, the Drude model is used to describe the conductor. The transverse electric and transverse magnetic contributions have very different character both in the low velocity (nonrelativistic) and high velocity (ultrarelativistic) regimes. Both numerical and analytical results are given. Most remarkably, the transverse magnetic contribution to the friction has a maximum for $|\mathbf{v}|<c$, and persists in the limit of vanishing resistivity for sufficiently high velocities. We also show how Vavilov-\v{C}erenkov radiation can be treated in the same formalism.