## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## Electric-field scr

Screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases (classical plasmas) and conduction electrons in semiconductors and metals. In a fluid composed of electrically charged constituent particles, each pair of particles interact through the Coulomb force,

$mathbf{F} = frac{q_1 q_2}{4piepsilon_0 left|mathbf{r} ight|^2}hat{mathbf{r}}$.

This interaction complicates the theoretical treatment of the fluid. For example, a naive quantum mechanical calculation of the ground-state energy density yields infinity, which is unreasonable. The difficulty lies in the fact that even though the Coulomb force diminishes with distance as 1/r², the average number of particles at each distance r is proportional to , assuming the fluid is fairly isotropic. As a result, a charge fluctuation at any one point has non-negligible effects at large distances.

In reality, these long-range effects are suppressed by the flow of the fluid particles in response to electric fields. This flow reduces the effective interaction between particles to a short-range "screened" Coulomb interaction.

For example, consider a fluid composed of electrons. Each electron possesses an electric field which repels other electrons. As a result, it is surrounded by a region in which the density of electrons is lower than usual. This region can be treated as a positively-charged "screening hole". Viewed from a large distance, this screening hole has the effect of an overlaid positive charge which cancels the electric field produced by the electron. Only at short distances, inside the hole region, can the electron's field be detected.

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