PlanetPhysics/Biot Savart Law

The Biot-Savart law is a [[../PrincipleOfCorrespondingStates/|physical law]] with applications in both [[../Electromagnetism/|Electromagnetism]] and aerodynamics. As originally formulated, the law describes the [[../NeutrinoRestMass/|magnetic field]] set up by a steady current density. More recently, by a simple analogy between [[../Magnetostatics/|magnetostatics]] and [[../LQG2/|fluid dynamics]], the same law has been used to calculate the [[../Velocity/|velocity]] of air induced by vortex lines in aerodynamic [[../SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence/|systems]].

The Biot-Savart law is fundamental to magnetostatics just as [[../CoulombsLaw/|Coulomb's law]] is to electrostatics. The Biot-Savart law follows from and is fully consistent with Amp\`ere's law, much as Coulomb's law follows from [[../GausssLaw/|Gauss' Law]].

In particular, if we define a differential element of current

$Id𝐥$

then the corresponding differential element of magnetic field is

$d𝐁=\frac{{\mu }_0}{4\pi }\frac{I𝐝l\times \widehat{𝐫}}{r^2}$

where

I is the current, measured in amperes

$\hat{r}$ is the unit displacement [[../Vectors/|vector]] from the element to the [[../CosmologicalConstant/|field]] point and the integral is over the current distribution

{\mathbf Examples}

 [[../QuarterLoopExampleOfBiotSavartLaw/|quarter loop example of Biot-Savart law]] [[../LoopExampleOfBiotSavartLaw/|loop example of Biot-Savart law]]

{\mathbf References}

[2] Jackson, D. "Classical Electrodynamics", John Wiley and Sons, Inc., 1975.

This entry is a derivative of the Biot-Savart law article [http://en.wikipedia.org/wiki/Biot-Savart\