Electromagnetic Waves along Wires

Electric energy cannot be transferred unless an electric and a magnetic field exist simultaneously. If these two fields are in time phase, the power is directly proportional to their product; if out of phase, it is proportional to their product and the cosine of the time phase angle between them. The maximum velocity with which an electromagnetic wave can travel is that of light, or approximately 186,300 miles, or 300,000,000 meters, per second. This applies to waves in free space; waves along wires travel more slowly.

Figure 1. The distribution of current and the accompanying magnetic field are shown by the dots and crosses adjacent to the wires. The distribution of the voltage and the accompanying electric field are shown by the arrows between wires.

In Fig. 1 is shown a portion of an infinitely long line connected to a source of alternating voltage. Current and voltage impulses will be distributed along the line somewhat as indicated. The dots (heads of arrows) and the crosses (tails of arrows) represent the magnetic field around the wires, and the arrows between wires represent the electric field. The magnitudes of the current and the voltage, and the corresponding intensity of the fields, are indicated by the relative number of arrows, dots, and crosses. The wavelength A is the distance between any two corresponding values, and the velocity of propagation V is the distance traveled per second. The wavelength is

since, at a frequency of / cycles per second, / complete waves are produced on the line per second, and these can travel only a distance of V miles during a second. An end view of the magnetic and the electric lines of force constituting an electromagnetic wave along two parallel wires is shown in Fig. 2.

Figure 2. End view of the line of Fig. 1, showing the electric field between the two wires, and the magnetic field around the wires.