# Coulomb law

Coulomb law is fundamental scientific concept about interaction of electric charges.

The special conserving quantity is postulated, called electric charge.

Potential energy of interaction of two charges \(q_1\) and \(q_2\) localised in regions small compared to the distance \(r\) between them, is postulated to be

\(\displaystyle U=k \frac{q_1 q_2}{r}\)

where \(k\) is fundamental constant determined by unit of measurement of the electric charge.

In the system SI, unit of charge is Coulomb, and

\(\displaystyle k=\frac{1}{4 \pi \varepsilon_0} \approx 8.9875517873681764\times 10^9~ \mathrm{Newton~ Meter^2~ Coulomb}^{-2} \)

## Additivity

Energy of interaction between charges is called electric energy; the corresponding interaction is called electromagnetic interaction.

Interaction between charges is postulated to be additive: the electric energy of system of \(N\) particles with charges \(q_n\), \(n=1..N\) is assumed to be

\(\displaystyle U=k \sum_{m < n}\frac{q_m q_n}{|\vec r_m-\vec r_n|}\)

where \(\vec r_n\) is vector of coordinates of \(n\)th charge.

In classical electrodynamics, there exist very interesting, difficult and important question about energy of interaction of a charge with itself. This question happen to be out of the range of applicability of the most of non-relativistic concepts of classical and quantum mechanics. (According to the First TORI axiom, each scientific concept has limited range of applicability.)

## Elementary charge

In quantum mechanics and theory of elementary particles, the charge is postulated to quantise, the corresponding fundamental constant is denoted with identifier ElectronCharge. For simplicity of programming, these two words can be written together.

\(e=\mathrm{ElectronCharge}\approx 1.602176487\times 10^{-19} \mathrm{Coulomb}\)

In order to avoid confusion with mathematical constants, in this case, \(\mathrm e=\exp(1)\approx 2.71\), the physical constant is written with Italics font.

Any concepts/theories with particles of fractional charge, for example, \(e/3\), are also allowed. In non–relativistic quantum mechanics, the postulate of charge as integer factor of \(e\) seems to be very good approach.

## Do physicians know physics?

Since century 20, the popular questions for students of medical institutes was:
**How many physicians know physics?**

The similar question refer to Mathematica about the example below:

Needs["PhysicalConstants`"] VacuumPermittivity N[VacuumPermittivity] ElectronCharge ElectronCharge^2/(4 Pi VacuumPermittivity )

The last line produces output \(\mathrm{ (2.30708\times 10^{-28}~ Coulomb^2~ Meter~ Volt)/(Ampere~ Second) }\)

instead of expected

\(\mathrm{ 2.30708\times 10^{-28}~ Joule~ Meter }\)

After a basic course of elementary school, a human have some idea, what are Coulomb, Meter, Volt, Ampere and Second, and may guess the correct answer. While, the same does not apply to the basic Mathematica software.

## References

http://www.physics.ru/courses/op25part2/content/chapter1/section/paragraph1/theory.html Подготовка к ЕГЭ 2015 онлайн. Глава 1. Электродинамика.

https://en.wikipedia.org/wiki/Coulomb%27s_law