Introduction to Numerical Electrostatics Using MATLAB

2The Uses of Electrostatics

Each topic discussed below is a sophisticated discipline in itself. The purpose of this chapter is to show where actual use of electrostatic analysis is involved in actual structures. Section 2.1, on basic circuit theory, is included because this is a discipline based on electrostatic (and magnetostatic) approximations whose use is implied in the functioning of the various structures discussed in subsequent sections.

2.1 Basic Circuit Theory

The speed of an electromagnetic wave in a vacuum (and essentially the same number in air) is 3 × 10⁸ m/s. A radio wave with a frequency of 1 MHz (one million cycles per second) has a wavelength of

(2.1)

If we are dealing with frequencies in this range or lower and with distances of, say, ≤1 ft, then we can ignore the propagation times along wires connecting various components and we can idealize components by pretending they’re infinitely small.

These assumptions allow us to define a branch of electrical science known as circuit theory, in which wires are ideal, lossless equipotential surfaces, with infinitely high signal propagation speed. This lets us define a list of components which are characterized by voltage–current terminal conditions.^1,2 Although we're introducing simple circuit theory only because some of its tools will be useful going forward, in principle all of circuit theory is a topic in electrostatics ...