Electric Field Strength Produced By An Individual Charge

Weʼll now consider the formula used to determine the electrical energy at a particular point. Since the total energy at the receiving antenna of an 802.11 device is the result of all of the individual points of energy, this fundamental equation becomes a key underlying component of the electromagnetic field itself.

Figure 5.2 The Strength of the Electric Field for an Individual Charge

This equation (Figure 5.2 above) is what a physicist might use to determine the strength of an electric field (E) produced by one individual charge. When the sum of all charges in a particular space are added together (vector addition) the result is the charge density in that space.

The first term ( -qerʼ/4πε0r2) is, essentially, taken directly from a calculation called Coulombʼs law. It tells us about a single electrical charge (-q; minus because itʼs a negative electrical charge). Charge is measured in units called Coulombs, where a single electron carries a charge of –1.602 X 10-19 Coulombs. The erʼ term is a unit vector in the direction from the point where E is being measured. So, thereʼs a charge, but the charge “feels like” a vector component of the charge because weʼre not “on” the charge itself but some particular direction (x-, y-, and z-axis location) away from the charge. This unit vector has a numerical value of 1 and simply points from the charge, back to the point, P, where the charge is being measured. The numerator of the first term, then, is the value of the charge and the direction in which the charge is located.

In the denominator you find, 4πε0r2. The constant ε0 (pronounced “epsilon naught”) is the constant of permittivity of free space. Permittivity, as has been discussed, is the characteristic of free space or of a substance (such as water) that determines the speed of light in that medium. In a vacuum light (and any electromagnetic wave) will travel at 299,792,458 meters/sec. It will travel slower in dense medium which is the basis for signal refraction. The frequency and wavelength of transmitted energy are directly related to each other, and to the speed of light. We write “vλ=c” where v is the frequency of the signal, λ (“lambda”) is the wavelength, and c is the speed of light in the medium. A 2.4 GHz carrier in an 802.11 network would have a wavelength of 12.5 cm in a vacuum, slightly less in the atmosphere (since c is slightly less). A 5.8 GHz carrier would have roughly a 5 cm wavelength in 802.11a.

The factor 4π speaks to the fact that the force is radiating outward from the charge in a spherical pattern and the surface area of a sphere is equal to 4πr2. Coulombʼs law says, then, that if you have a particular charge being measured from a particular direction, the strength will be the result of the charge being spread out over the surface of a sphere of a particular radius and will be affected by the permittivity of the medium.

With regard to atmospheric propagation in free space (a vacuum) ε0 = 8.987552 X 10-12 Farads / meter. The Farad (F) is the unit of capacitance. With 1 F of capacitance a single coulomb of charge can be held at one volt. A coulomb of charge is 6.25 X 1018 electron volts (the electrical potential

Copyright 2003 - Joseph Bardwell