Penetration of electromagnetic velocity fields through a conducting wall of finite thickness

The penetration of electric and magnetic velocity fields through a conducting wall (with epsilon = 1, mu = 1) when a nonrelativistic charged particle is traveling outside parallel to the wall is calculated for a good conductor in a perturbation analysis through first order in the velocity ratio beta = v/c. It is found that the magnetic field behind the conducting wall is of a universal character depending only on the displacement of the field point from the charged particle outside the wall; the field is modified by the presence of the conducting wall but is independent of the conductivity, the thickness, or the relative placement of the wall. Within the conductor, the magnetic field depends upon the thickness of the wall but not upon the conductivity of the wall. In front of the conducting wall, the magnetic field is independent of the conductivity or the thickness of the wall. The electric field inside and outside the conducting wall depends upon the conductivity and thickness of the wall. In the region behind the wall, the electric field falls off as r(-3). The currents in the conducting wall are independent of conductivity but depend upon the thickness of the wall. The electric field in front of the wall exerts a dragging force on the passing charged particle, providing the energy balance for resistive heating in the wall. This dragging force increases as the thickness of the wall decreases. The present general analysis extends earlier work in the Literature that treats the special cases of an infinitely thick conducting wall and of a thin perfectly conducting wall. The ideas involved are unfamiliar to many physicists, who are not aware that electromagnetic velocity fields have an algebraic behavior inside conductors, which is completely different from the familiar exponential damping of electromagnetic wave fields. The ideas are of interest in connection with the electromagnetic shielding of systems from electromagnetic fields of passing charges and in connection with the Aharonov-Bohm effect where charged particles pass close to conducting solenoids.