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



It seems the only reason why students might be confused by the 4*pi in
Coulomb's law is because there is no 4*pi in the gravitational law.
Perhaps we should introduce the 4*pi in the gravitational law. Would it
be any less abstract for students to have gravity inversely proportional
to surface area?

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| Robert Cohen Department of Physics |
| East Stroudsburg University |
| bbq@esu.edu East Stroudsburg, PA 18301 |
| http://www.esu.edu/~bbq/ (570) 422-3428 |
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On Mon, 22 Jan 2001, Ludwik Kowalski wrote:

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