of 6.25 billion billion electrons). The permittivity constant for the medium refers to the capacity of the medium to impede the propagation of a charge. If medium “A” can hold a greater charge than medium “B” the value of ε is greater for medium “B”. On a hot dry day, with a high pressure weather system over an area, the air is less dense than on a damp, foggy winter day when thereʼs a low front getting ready to bring rain into the area. These changes can have dramatic impacts on the propagation characteristics of an electromagnetic wave.

Under normal conditions the value of ε is very close to ε0. and the denominator in Coulombʼs law, (given as 1/4πε0) is treated as a constant (denoted by “k”) with a value of 8.987552 Nm/c2 (Newton meters / speed of light in the medium, squared). As a result the first term of the energy equation could be rewritten as –qerʼ/kr2.

Time Delay and the Retarded Wave

Maxwell discovered that Coulombʼs contribution was, as weʼve said, incomplete. This is where the next parts of the field energy calculation come into play. Letʼs assume that a measurement is being done at some particular place that weʼll denote as (x,y,z). Weʼre measuring E at location (x,y,z) which, by the way, is located in the erʼ (unit vector) direction from where weʼre measuring. (There is no (x,y,z) in the formula, weʼre just using this point to refer to where E is being measured). Now, the charge –q is assumed to be moving, vibrating in some particular way and at some particular

frequency (resulting in some particular wavelength). An 802.11b or 802.11g device transmits a carrier frequency close to 2.4 GHz which is 2,400,000,000 vibrations (cycles) per second. This moving charge is producing a magnetic field and an accompanying electric field E.

The problem is that at (x,y,z) we cannot determine what –q is doing right now. The influence of –q on the space around it can not travel faster than the speed of light in the medium, denoted by “c”. Consequently, when we observe a particular –q at P weʼre observing an effect that actually happened in the past. It didnʼt happen very far in the past, but in the past nonetheless. This is a very mysterious thing and itʼs referred to as a retarded wave. When a wave is measured, the measurement is always telling you how things were a moment ago. Of course, if weʼre talking about electromagnetic measurements of energy coming from our sun then the time delay (called retarded time) is roughly 8- minutes. If weʼre measuring microwave radiation coming from an object in a remote galaxy, then we could have retarded time of thousands of years (for an object that was thousands of light years away).

The fact that the wave is being measured with retarded time is accounted for in the second term of the energy equation, rʼ/c. The figure (5.2) is reproduced again below to help you avoid flipping pages as you read this paper.

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

The wave retardation factor (time delay) is rʼ/c. What appears in the formula is the apparent distance that the charge is from (x,y,z) at the point of measurement.

Copyright 2003 - Joseph Bardwell