perkee's blog

LaTeX and Electromagnetics

maybe you have an electromagnetics final in 7.5 hours like I do. maybe you want a study sheet. Maybe I have one for you, because I’ve got the LaTeX if you’ve got the time…

\documentclass[11pt]{amsart}
\usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                   % ... or a4paper or a5paper or ... 
%\geometry{landscape}                % Activate for for rotated page geometry
%\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{epstopdf}
\usepackage{amsmath}
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}

%%%%%%%%%%%   Bold style  Vectors%%%%%%%%%%%%%
\newcommand{\vect}[1]{\ensuremath{\boldsymbol{#1}}}
\newcommand{\unit}[1]{\ensuremath{\boldsymbol{\widehat{#1}}}}
\newcommand{\del}{\ensuremath{\boldsymbol{\nabla}}}

%%%%%%%%%%% arrow style vectors %%%%%%%%%%%%%%
%\newcommand{\vect}[1]{\ensuremath{\overrightarrow{#1}}}
%\newcommand{\unit}[1]{\ensuremath{\widehat{#1}}}
%\newcommand{\del}{\ensuremath{\nabla}}

\newcommand{\dotp}{\ensuremath{\!\cdot\!}}

\begin{document}
\section{Electric}

\begin{description}
	\item[Field due to point charge] \hfill $\vect{E}=\frac{Q\unit{R}}{4\pi\epsilon R^2} = \frac{Q\vect{R}}{4\pi\epsilon R^3}$
	\item[Electric Flux Density] \hfill $\vect{D} = \epsilon_0\vect{E}  + \vect P= \epsilon\vect{E}=\frac{Q\unit{R}}{4\pi R^2} $
	\item[Gauss's Law] \hfill $Q=\oint\vect{D}\dotp\vect{ds} = \oint\vect{D}\dotp\unit{n}ds  = \int\del \dotp\vect{D}dv = \int\rho_vdv$ \\ \hfill (``$v$'' as in volume.)
	\item[Voltage] \hfill $V_{1-2}=-\int_2^1\vect{E}\dotp\vect{dl}$
	\item[Capacitance] \hfill $C=\frac{Q}{V}$
	\item[Charge Density] ~
	 	\begin{description}
	 		\item[Surface] \hfill $\rho_s=\frac{Q}{S}$
	 		\item[Volume] \hfill $\rho_v=\del\dotp\vect{D}$
	 		\item[Polarization Surface] \hfill $\rho_{\textit{ps}}=\vect{P}\dotp\unit{n}$
			\item[Polarization Volume] \hfill $\rho_{\textit{ps}}=-\del\dotp\vect{P}$
	 	\end{description}
	\item[Polarization] \hfill $\oint\rho_{\textit{ps}}\vect{ds}+\int\rho_{\textit{pv}}\vect{dv} = 0$
	\item[Boundary Conditions]  ~
		\begin{description}
			\item[Tangential] \hfill $E_{t1} = E_{t2}$
			\item[Normal] \hfill $D_{n1} - D_{n2}=\rho_s$
		\end{description}
	\item[Energy Density] \hfill $W=\frac{1}{2}\vect{D}\dotp\vect{E}=\frac{1}{2}\epsilon\vect{E}\dotp\vect{E}$
	\item[Total Energy] \hfill $W=\frac{1}{2}\int_{v'}\rho_vvdv = \frac{1}{2}\int_{v'} \epsilon \vect{E}\dotp\vect{E} dv = \frac{1}{2}CV^2= \frac{1}{2}QV=\frac{1}{2}\frac{Q^2}{C}$
	\item[Force] \hfill $\vect{F}=-\del W=QE$
	\item[Poisson's Equation] \hfill $\del^2V=\frac{-\rho_v}{\epsilon}$
	\item[Laplace Equation] \hfill $\del^2V=0$
\end{description}
\section{Current}
\begin{description}
	\item[Current Density] \hfill $\vect J = \sigma \vect E $
	\item[Resistance] \hfill $ R = \frac{l}{\sigma s}$
	\item[Calculus with $\vect J$] \hfill $ \del \dotp \vect J = 0$
	\item[Current Boundary Conditions]  ~
		\begin{description}
			\item[Tangential] \hfill $\frac{J_{t1}}{\sigma_1} = \frac{J_{t2}}{\sigma_2} $
			\item[Normal] \hfill $J_{n1} = J_{n2}$
		\end{description}
\end{description}
\section{Magnetic}
This will be a long night\dots
\end{document}