Getting back to Maxwell's equations, we explored what happens in a vacuum with no charges nor currents [Transparancy 1]. It turns out that the electric and magnetic vector fields satisfy a wave equation.
In order to explore solutions of this wave equation, we assumed that the electric vector field has a cosine and sine term [Transparancy 2]. It was then shown that this solution satisfies the wave equation. A relation was found [Transparancy 3] between the wave speed (speed of light) and the electrical permittivity of space and the magnetic permeability of space. It was also shown that the direction of the electric field is perpendicular to the direction of propagation of the wave. The same relation also holds for the magnetic field, which can be shown to be perpendicular to the electric field. The final result is a transverse electromagnetic wave propagating through empty space!
This is historically a very profound result, which led to useful things like radar, microwave ovens, and cell phones.
(You will find two versions -- a "screen" version, which is 400 pixels wide and a corresponding number of pixels long, at a resolution of 100 by 100 dots per inch, and a "print" version, which is generally between 8 and 8.5 inches wide and up to 11 inches long, also at a resolution of 100 by 100 dots per inch. The screen versions generally have a file size of between 60 and 75 K, which downloads reltively quickly. The print versions generally have a file size of between 170 and 225 K, which takes a bit longer to download.)
