Electric Potential



Recall the developmental history of electrostatics.

  1. Charges exist.
  2. Charges exert forces on each other.
  3. This force appears to exert itself across distances of any size.

You and I have no problem with this idea, but in the day, this was derisively called "action at a distance". To get around the action at a distance problem and to avoid the conceptual and mathematical problems of dealing with this otherworldly force, Michael Faraday invented the electric field and the world was satisfied.

Well, satisfied for awhile. Once Faraday invented the idea of the field, it became a great conceptual hit and everybody was happy for until … Until somebody noticed that the field was a vector quantity and they remembered that vectors were cumbersome and difficult to deal with mathematically. Conceptual ease was gained, but practical ease was unchanged. Damn those scientists. Always looking for the best of all possible worlds. They wanted something both conceptually and mathematically simple to deal with. Such temerity!

Believe it or not, a solution was at hand. Of course we only know this to be the case with the fortune of hindsight. The problem has already been solved, which makes it seem to us like no big deal. But it took years of thinking and years of hard, deliberate work before the next step was taken.

What are field lines if not some kind of flow pattern? Field lines "flow" from positive charges to negative charges. They occupy space much like the flow lines associated with other phenomena. Think for a moment, of other phenomena that exhibit flow and think of what it is that causes them. This will be the answer to our conceptual problem.

Let's set up a table that compares similar phenomena. In all cases, there will be some thing that flows and some cause of the flow.

the flow of … is caused by a difference in …
a river (liquid water) altitude
the wind (atmospheric gases) atmospheric pressure
heat (internal energy) temperature
dissolved substances (solutes) concentration

Surely, field lines (or charges, if you prefer) must flow under the influence of something. Well of course yes, why else would I be telling you any of this? What "causes" electric field lines to "flow"?

the flow of … is caused by a difference in …
electric field lines (test charges) electric potential

Now you have to ask yourself what "electric potential" is.

Random junk

millikan's experiment

Robert Millikan (1865–1953) United States