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

then the corresponding differential element of magnetic field is

where

I is the current, measured in amperes

r is the unit displacement vector from the element to the field point and the integral is over the current distribution

Examples

• quarter loop example of Biot-Savart law
• loop example of Biot-Savart law

References

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

This entry is a derivative of the Biot-Savart law article from Wikipedia, the Free Encyclopedia. Authors of the orginial article include: Salsb, Tim Starling, Metacomet, JabberWok and Toby Bartels. History page of the original is here