ElectricFieldOfALineOfCharge 2006-09-21 14:10:33 2006-09-21 14:10:33 Topic Electric Field % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) \usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \section{The Electric Field of a Line of Charge} Calculating the electric field due to a non-moving continuous distribution of charge is a common task in electrostatics. Unfortunately, without resorting to numerical methods, we are limited to simple geometries and field points that rely on symmetry in order to make the integrals tractable. Here we will examine the electric field due to a continuous line of charge on a line segment of length L. Analytically, we will compute the E-field at two different field points and then look at computing the entire field using a numerical technique. \subsection{Center Line} The electric field at a height y above the line segment and on the center line as shown in below figure is straight forward and is one of the basic examples given in [1][2][3]. \begin{figure} \includegraphics[scale=.8]{ElectricFieldLineSegment.eps} \vspace{20 pt} \end{figure}