Talk:PlanetPhysics/Coulomb's Law

Original TeX Content from PlanetPhysics Archive
%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: Coulomb's law %%% Primary Category Code: 41.20.Cv %%% Filename: CoulombsLaw.tex %%% Version: 1 %%% Owner: bloftin %%% Author(s): bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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Coulomb's law describes the \htmladdnormallink{electrostatic force}{http://planetphysics.us/encyclopedia/WheatstoneBridge.html} between \htmladdnormallink{Electric Charges}{http://planetphysics.us/encyclopedia/Charge.html}. Coulomb was the first scientist to measure the force using a torsion balance and he discovered that the attraction or repulsion force increases or decreases inversely as the \htmladdnormallink{square}{http://planetphysics.us/encyclopedia/PiecewiseLinear.html} of the distance between the charges. As an equation Coulomb's law is given as

\begin{center} $F = k \frac{q_1 q_2}{r^2}$ \end{center}

This equation only gives the \htmladdnormallink{magnitude}{http://planetphysics.us/encyclopedia/AbsoluteMagnitude.html} of the force, but we must also take into account the direction of the force. Similar to gravity, the force between the charges acts along a line between them. Coulomb's law in \htmladdnormallink{vector}{http://planetphysics.us/encyclopedia/Vectors.html} form is

\begin{center} $ \vec{F} = k \frac{q_1 q_2}{r_{12}^3} \vec{r}_{12} $ \end{center}

Some explanation is needed for the variables. $r_{12}$ is the distance between the two charges. The direction of the force is taken into account through the \htmladdnormallink{unit vector}{http://planetphysics.us/encyclopedia/PureState.html} $\hat{r}_{12}$ which will point towards the other charge or in the oppososite direction depending on attraction or repulsion. So to go from the first equation we add the unit vector

\begin{center} $ \vec{F} = k \frac{q_1 q_2}{{r^2}_{12}} \hat{r}_{12}$ \end{center}

To get a unit vector we divide the vector between the charges by its magnitude

\begin{center} $\vec{r}_{12} = r_{12} \hat{r}_{12}$ \end{center}

so the unit vector is

\begin{center} $\hat{r}_{12} = \frac{\vec{r}_{12}}{r_{12}} $ \end{center}

repacing the unit vector with the above equation yields the vector form of Colomb's Law.

More to come on how Coulomb used a torsion balance to come up with this relationship...

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