Re: Potential of a point charge

[John Denker <jsd@AV8N.COM>]

Quoting Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>:

> I agree that the minus sign in the definition is confusing. Especially
> when the author tells us "between two points A and B" as if any
> arbitrary two points could be chosen. In reality (and this should be
> clearly stated before the definition is introduced) the point B is
> "downhill" electrically speaking, with respect to the point A. In other
> words, the potential energy increase is negative when the dot product
> is positive (work done 'by the field" and not "on the field").

That remark represents a considerable change in topic, but
that's OK.

I don't think I agree with the statement that B has to be
``downhill'' w.r.t A.  Gauge invariance and all that.

In the problem Rick asked about, people commonly choose the
gauge such that the potential goes to zero at r=infinity.
But this is absolutely not mandatory.

The general, gauge-invariant way to look at it is to say that
the potential drop from A to B is
   1/r_A - 1/r_B
and there is not the slightest reason to require or even
suspect that B is downhill from A.