Biot-Savart law

Biot-Savart law, in electromagnetics, it describes the magnetic field set up by a steady current density.

Another equation used, that gives the magnetic field due to each small segment of current, is the Biot-Savart law.

The Biot-Savart law is also used to calculate the velocity induced by vortex in aerodynamic theory.

Alternatively, introductory treatments of magnetism introduce the Biot-Savart law, which describes the magnetic field associated with an electric current.

The Biot-Savart law is fundamental to magnetostatics, playing a similar role to Coulomb's law in electrostatics.

Maxwell's equations, which simplify to the Biot-Savart law in the case of steady currents, describe the origin and behavior of the fields that govern these forces.

Start with the formula for the on-axis field due to a single wire loop [1] (which is itself derived from the Biot-Savart law):

Jean-Baptiste Biot and Félix Savart demonstrate the Biot-Savart law in electromagnetism.

It can be shown from the Biot-Savart law that the magnetic field at a given distance () from an infinite current-carrying wire is given by:

In railgun physics, the magnitude of the force vector can be determined from a form of the Biot-Savart law and a result of the Lorentz force.

If there is free current, one may subtract the contribution of free current per Biot-Savart law from total magnetic field and solve the remainder with the scalar potential method.

In electromagnetism, magnetostatics equations such as Ampère's Law or the more general Biot-Savart law allow one to solve for the magnetic fields produced by steady electrical currents.

Finally, Jean-Baptiste Biot and Félix Savart discovered the Biot-Savart law in 1820, which correctly predicts the magnetic field around any current-carrying wire.

Third, the tangential induction factors can be solved with a momentum equation, an energy balance or orthognal geometric constraint; the latter a result of Biot-Savart law in vortex methods.

The general formulation of the magnetic force for arbitrary geometries is based on line integrals and combines the Biot-Savart law and Lorentz force in one equation as shown below.

These equations are the time-dependent generalization of Coulomb's law and the Biot-Savart law to electrodynamics, which were originally true only for electrostatic and magnetostatic fields, and steady currents.

The second describes the creation of a static magnetic field B by an electric current I of finite length dl at a point displaced by a vector r, known as Biot-Savart law:

Further, Ampère derived both Ampère's force law describing the force between two currents and Ampère's law which, like the Biot-Savart law, correctly described the magnetic field generated by a steady current.

Using the Biot-Savart law, it can be shown that the magnetic flux density ' induced by a solenoid of effective length ' with a current ' through ' loops is given by the equation:

Importantly, this theory does not predict an expression like the Biot-Savart law and testing differences between Ampere's law and the Biot-Savart law is one way to test Weber electrodynamics.

The physical origin of this force is that each wire generates a magnetic field, as defined by the Biot-Savart law, and the other wire experiences a magnetic force as a consequence, as defined by the Lorentz force.

The Biot-Savart law can be used in the calculation of magnetic responses even at the atomic or molecular level, e.g. chemical shifts or magnetic susceptibility, provided that the current density can be obtained from a quantum mechanical calculation or theory.

The Biot-Savart law is used to compute the magnetic field generated by a 'steady electric current', i.e. a continual flow of electric charge, for example through a wire, which is constant in time and in which charge is neither building up nor depleting at any point.