BiotSavartLaw 2006-01-14 18:47:52 2006-01-14 18:48:31 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 The Biot-Savart law is a physical law with applications in both electromagnetism and aerodynamics. As originally formulated, the law describes the magnetic field set up by a steady current density. More recently, by a simple analogy between magnetostatics and fluid dynamics, the same law has been used to calculate the velocity of air induced by vortex lines in aerodynamic systems. The Biot-Savart law is fundamental to magnetostatics just as Coulomb's law is to electrostatics. The Biot-Savart law follows from and is fully consistent with Ampère's law, much as Coulomb's law follows from Gauss' law. In particular, if we define a differential element of current $$I d{\bf l} $$ then the corresponding differential element of magnetic field is $$ d{\bf B} = \frac{\mu_0}{4 \pi}\frac{I {\bf dl} \times {\bf\hat{r}}}{r^2} $$ where I is the current, measured in amperes $\hat{r}$ is the unit displacement vector from the element to the field point and the integral is over the current distribution This entry is a derivative of the Biot-Savart law article \PMlinkexternal{from Wikipedia, the Free Encyclopedia}{http://en.wikipedia.org/wiki/Biot-Savart\%27s_Law}. Authors of the orginial article include: Salsb, Tim Starling, Metacomet, JabberWok and Toby Bartels. History page of the original is \PMlinkexternal{here}{http://en.wikipedia.org/w/index.php?title=Biot-Savart_law\&action=history} {\bf References } [2] Jackson, D. "Classical Electrodynamics", John Wiley and Sons, Inc., 1975.