PlanetPhysics/Biot Savart Law

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 Amp\`ere's law, much as Coulomb's law follows from Gauss' Law.

In particular, if we define a differential element of current

$Id{\mathbf {l} }$

then the corresponding differential element of magnetic field is

$d{\mathbf {B} }={\frac {\mu _{0}}{4\pi }}{\frac {I{\mathbf {d} l}\times {\mathbf {\hat {r}} }}{r^{2}}}$

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

{\mathbf Examples}

 quarter loop example of Biot-Savart law 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\