Re: On 1/4*Pi in Coulomb's law

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Joel Rauber wrote:

> John wrote in part:
>
> > f) There is no logical basis for giving Coulomb's law
> > priority over all the
> > other laws, and insisting that it be simplified no matter what.
>
> In the typical intro text book there is plenty of logical basis for doing
> this: it is the first topic covered in the study of electro-magnetic
> phenomena.  This may not be sufficient to warrant overturning SI,
> but it is logical.

Yes, and this was my main point. I agree that 4*Pi can not be
eliminated from physics because it is the solid angle of the 3D
space in which everything happens. Likewise with 2*Pi in 2D.

If there is no 4*Pi in Coulomb's law then it appears naturally
in Gauss law, and vice versa, as emphasized by John. If we
were to start with Gauss law as it is written in SI, then 4*Pi
would appear when Coulomb's law is derived from the initial
Gauss law.

But we do not teach physics this way in elementary courses.
For us Coulomb's law is the starting point. Students know
nothing about Gauss law at this time. Heaviside introduced
4*Pi into the Coulomb's law to make it disappear in the Gauss
law. That was his main motivation; right? But how can one
use this reasoning with somebody who does not know Gauss
law? We do not. We say "accept the 4*Pi factor because it
will benefit us in the future." That is how an element of
apparent dogmatism is introduced. It is not a scientific
topic, it is a pedagogical topic.
Ludwik Kowalski