coulomb’s law is a principle that deals with the force that two charged particles exhibit to each other.

## constituents

- \(k\), Coulomb’s Constant, found roughly to be \(9 \times 10^{9} \frac{N m^{2}}{C}\)
- \(q_{1,2}\), the charge of the two particles you are analyzing
- \(r\), distance between particles

## requirements

\begin{equation} \vec{F_{E}} = k \frac{q_1q_2}{r^{2}} \end{equation}

## additional information

### interpreting signs on \(F_{e}\)

- negative: attraction force between changes (the points have opposite signed charges, and so attract)
- positive: repulsion force between changes (the point have the same signed change, so repel)

### alternative formulation of Coulomb’s Law

The law is often redefined with the language of the premittivity of free space:

\begin{equation} \vec{F_{E}} = \frac{1}{4\pi \epsilon_{0}} \frac{q_1q_2}{r^{2}} \end{equation}

### superposition

The net electric force on a test change is simply the sum of the electric forces which other particles exhibit on the test change. That is:

\begin{equation} F_{on\ 2} = F_{1 \to 2} + F_{3 \to 2} \end{equation}