Coulomb's law

Claimed by Spencer Boebel (Fall 2023)

Coulomb's Law

Overview

Coulomb's Law states that [math]\displaystyle{ \vec{F}_{on1} = {\frac{q_{1}q_{2}}{4\pi\epsilon_{0}|\vec{r}_{12}|^2}}\hat{r}_{12} }[/math] , where [math]\displaystyle{ \vec{F}_{on1} }[/math] is the force on charge [math]\displaystyle{ q_{1} }[/math] by charge [math]\displaystyle{ q_{2} }[/math], [math]\displaystyle{ |\vec{r}_12| }[/math] is the distance between the charges, and [math]\displaystyle{ \hat{r}_{12} }[/math] is the unit vector pointing from [math]\displaystyle{ q_{1} }[/math] to [math]\displaystyle{ q_{2} }[/math]. In words, it says that the force on one charged particle ([math]\displaystyle{ A }[/math]) by another charged particle ([math]\displaystyle{ B }[/math]) is directed at [math]\displaystyle{ A }[/math], is jointly proportional to the charges themselves (signs included), and is inversely proportional to the distance between [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] squared. Coloumb's Law holds only when the two particles are at rest, and it can be derived from Gauss's law, which is one of Maxwell's Equations. Coloumb's Law can be used to analyze electrostatic situations such as the movement of a charge suspended between two plates as well as determining the electric field from a given charge distribution.

Main Idea

A Mathematical Model

According to [1],

A Computational Model

History

Coulomb's Law was first formulated in

See Also

-Biot-Savart Law -Law of Superposition -Gauss' Law

References

1. https://www.feynmanlectures.caltech.edu/II_04.html