Dynamic shielding of a charge in a metal

A discussion of the shielding of a charged particle in a current-carrying conductor is given that is based on the linearized Thomas-Fermi approximation. An expression for the force on a particle of charge q is obtained from which the value of the electric field E_c in the conductor may be found:

$\text{E}{}_{\mathrm{c}}\text{=}\text{lim}\text{q→0}\text{F}{}_{\mathrm{q}}\text{/q}$

It is shown that the force on the particle has the form $\text{F}{}_{\mathrm{q}}\text{= q}\text{E}{}_0\text{× (1 + γ(}\text{q}\text{e}\text{) + …}$ to second order in the charge q, where E₀ is the electric field at large distances from q, e is the charge of the carrier, and γ is a material-dependent constant. The shielding correction has the character of a “wind-force,” and the electric field in the conductor is given by Ec = E₀.