Over the next few months, I would like to examine the role of concepts such as "electric charge", the "electric field" and the "magnetic field" in classical electromagnetism.
My aim is to understand how these concepts are used, together with experimental findings, to arrive at some of the laws of classical electromagnetism, including Maxwell's equations and the "electric length contraction" of moving bodies by the relativistic factor.
I have decided to base my investigations on William Geraint Vaughan Rosser's book Interpretation of Classical Electromagnetism (1997).
Of the three concepts mentioned, that of "charge" is perhaps the most fundamental and seemingly straightforward. It is closely tied to the notion of "particles", which are said to be carriers of "charge" if they show characteristic forms of attraction or repulsion. Rosser speaks of "charged atomic particles such as electrons and positive ions". He says that, in his book, such "classical point charges" will be treated as "continuous charge distributions of exceedingly small but finite dimensions" (p. 2).
The suggestion is that "charge" is a real attribute of at least some particles. These particles and the "charge" they carry are thought to occupy an "exceedingly small" amount of space.
A first difficulty presents itself here if we consider that the attraction or repulsion between such "point charges" is effective over distances which are very large compared to the "exceedingly small" size of the charges. If it is "charge" which is responsible for this attraction/repulsion, should we not conclude that, far from occupying a very small amount of space, "charge" is something which is spread out over all of space, although its intensity or density decreases as we move away from a charged particle's point-like centre?
Whatever the merits of such an approach may be, it does not seem to have been explored in the context of classical electromagnetism. So, what is it in classical electromagnetism that accounts for the action of "charge" over large distances? Is it perhaps the "electric field"? In my next post, I will begin to examine what role this concept plays in Rosser's interpretation of classical electromagnetism.
