Biot-Savart's Law

The Biot-Savart Law describes the magnetic field set up by a steadily flowing line current: the field produced by a current element <math>d\vec l<math> is

<math> d\vec B = K_m \frac{Id\vec l \times \hat r}{r^2} <math>

where <math>K_m = \frac{\mu_0}{4\pi}<math> is the magnetic constant, I is the current and <math>\hat r<math> is the unit vector from the element to the field point. Hence, integrating, the field produced by current flowing in a loop is

<math> \vec B = K_m I \int \frac{Id\vec l \times \hat r}{r^2}. <math>

The Biot-Savart law is fundamental to magnetostatics just as Coulomb's law is to electrostatics. It is equivalent to Ampère's law.

The Biot-Savart law is also used to calculate the velocity induced by vortex lines in Jean Baptiste Biot, Felix Savart, magnetism, vorticity