Coulomb law

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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 $d_2$ 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} $

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 with respect to the example below:

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.



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