OffAxisExampleOfBiotSavartLaw 2006-03-11 12:29:40 2006-03-11 12:57:50 Example Biot-Savart law % 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 $r = x \hat{x} + z \hat{z}$ \\ $r' = r' \cos \phi' \hat{x} + r' \sin \phi' \hat{y}$ \\ $dl = -r d\phi' \sin \phi' \hat{x} + r d\phi' \cos \phi' \hat{y} $\\ $ r - r' = (x - r' \cos \phi') \hat{x} + r' \sin \phi' \hat{y} + z \hat{z}$ \\ $ dl \times (r - r') = zr' d\phi \cos \phi' \hat{x} + zr'd\phi \sin \phi' \hat{y} + [- x r' d\phi cos\phi' + r'^2 d\phi] \hat{z} $ \\ $ \left | r - r' \right | = =$