The most important component in electric guitar history was, of course, advances in the understanding of elctricity and electro-magnetic theory. This critical physical phenomenon made possible many advances such as electric lights, electric motors, etc. Without it there would have been no electric guitar.
After being fired by National String Instrument Company, George Beauchamp
(pronounced "Beachum") began looking for other ways to increase the volume of the
guitar. By this time it was well known that passing a wire through a magnetic field
would induce an current in the wire and, therefore, an electric field around the wire.
If the wire was vibrating, this would produce an alternating current(in other words, the direction of
the current would flip flop as the wire vibrated back and forth) and, as a consequence, the direction
of the electric field produced would also alternate. This was a critical component in the beginnings
of electric guitar history.
Note this phenomenon was well understood and was the basis of the operation of electric motors, phonograph needles, etc. Beauchamp realized that if this principle could be applied to steel guitar strings and, that if a device could be constructed that could pick up the vibrations of the strings individually, the vibrations could be converted to an electric current that could be sent to and amplified by one of the tube type amplifiers that were currently being used by the PA and radio systems of the day. This would successfully amplify the guitar.