Introduction to Numerical Electrostatics Using MATLAB

17Electrostatic Forces

17.1 Introduction

The basis of electrical phenomena is the Coulomb force –– the force exerted by a charged particle on other charged particles. The electric field due to a collection of charged particles is defined as the force on a small “test” particle, such as an electron. The charge of the test particle is assumed to be so small as to allow virtually no perturbation of the electric field due to the test particle’s presence. In practice, this is almost always an excellent approximation for use with low-density electron charge distributions (low density here means that the motion of the electrons is not influenced by that of the other electrons). Typically, electronic devices are built in high-vacuum containers (CRT displays, scanning electron microscopes), and electron motion in a static electric field is an exercise in solving Newton’s equations. We solve the following equation, usually numerically, where is the vector of the position coordinates of the charged particle:

(17.1)

When the electric field forces are strong enough to actually move one of the electrodes, then we cannot use equation (17.1), which assumes that the electric field is constant in time. Instead, we must use the principle of virtual work,¹ which states that for a movement (of an electrode ...