[[Electrodynamics MOC]]
# Coulomb's law
**Coulomb's law** describes the force experienced by a test charge $Q$ due to a single source charge.
$$
\begin{align*}
\vab F = \frac{1}{4\pi\epsilon_{0}} \frac{qQ}{\Sr^2} \unitv\SR
\end{align*}
$$
where $\vab\SR$ is the vector from $Q$ to $q$.[^2013]
The [[Principle of Superposition]] allows this to be generalised to a distribution of charge by
$$
\begin{align*}
\vab F = \frac{Q}{4\pi \epsilon_{0}} \iiint _{\mathbb{R}^3}  \frac{\rho(\vab r')}{\Sr^2} \unitv\SR \,d\tau'
\end{align*}
$$
It quickly becomes pertinent to introduce the idea of the [[Electric field]].

[^2013]: 2013\. [[@griffithsIntroductionElectrodynamics2013|Introduction to electrodynamics]], p. 60 (§2.1.2)
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