# Coulomb interaction

Written by Yuhang Jin, AP225 2011 Fall.

## Introduction

Coulomb interaction is the electrostatic interactions between electric charges, and follows the Coulomb's law, which is a basis of classical electrodynamics. In general, Coulomb interaction can manifest itself on various scales from microscopic particles to macroscopic bodies. The microscopic theory of Coulomb interaction has been developed in the frame of quantum field theory.

## Basic formulae

The electrostatic interaction of two point charges <math>q_1</math> at position <math>\mathbf r_1</math> and <math>q_2</math> at position <math>\mathbf r_2</math> is described by the Coulomb's law:

<math>\mathbf F=\frac{1}{4\pi\varepsilon_0}\frac{q_1q_2(\mathbf r_1-\mathbf r_2)}{|\mathbf r_1-\mathbf r_2|^3}</math>,

where <math>\mathbf F</math> is the electrostatic force, and <math>\epsilon_0</math> is the vacuum permittivity, which has a value of <math>8.85\times10^{-12}</math> approximately.

## Keyword in references:

Photonic Properties of Strongly Correlated Colloidal Liquids