# The Coulomb Force

Also known as Coulomb’s Law, this Force affects you everyday (you are made up of static charges, ain’t ya?). You’ve heard of this one… yeeeeah you have, at least for me, it’s because I can never remember where the hell the “u” in Coulomb is supposed to go.

Before the “l”, the answer is before the “l”, goddamn it.

This guy Coulomb was investigating Electric Charge back around the American Revolution (think Ben Franklin – it makes some sense) and back then, the conventional way of doing this was to rub your socks or something against certain objects to see if they became statically charged.

Needless to say, Coulomb figured out what pair of socks worked best, and got his research under way.

It’s an Inverse Square Law like Newton‘s Universal Law of Gravity, and actually it looks an awful lot like it too. The law, as stated in scalar form, gives the Coulomb force between two charges (denoted by capital “Q”): $F=k_e\frac{Q_1Q_2}{r^2}$ where “k” is Coulomb’s Constant.

The vector correct version of the force on Q1 by Q2 is: $\vec{F}_1= k_e{\frac{Q_1Q_2}{|{r^2}_{1,2}|}}\vec{r_{2,1}}$

You can get this “k” empirically (via careful experiment) but it can also be found theoretically to a precise value: $k_e = \frac{1}{4{\pi}{\epsilon}_0}$ where ${\epsilon}_0$ is the Permittivity of Free Space.

Leaving us with $F = \frac{1}{4{\pi}{\epsilon}_0}\frac{Q_1Q_2}{r^2}$

Want a derivation? There ya go.