Houjun Liu

Coulomb's Law

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


  • \(k\), 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


\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}


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}