Coulomb law, k costant

[Bern123]

What k mean in coulomb law? it's 1/(4π*ε) but why is in this form? 4π it's related to the shape of an atom?

 

[arildno]

Basically "k" has been given this strange, nonintuitive shape so that deep and fundemental results in electromagnetism look cleaner on the paper

$$4\pi$$ is the surface area of a unit sphere.

The "e" is the "vacuum permittivity", closely related to the speed of light in vacuum, "c", through the formula:
$$\epsilon_{0}\mu_{0}=\frac{1}{c^{2}}$$,
where $\mu_{0}$ is called the "magnetic constant". (That formula is now used as the DEFINITION of our "e")

When we look at propagation of light waves and electromagnetic waves in general, our number "e" is so closely related to it that it pops up everywhere, and therefore, Coulomb's law has been written in such a way to make that important constant explicit, rather than using a fuzzy "k".