Biot-Savart Law Guide, Meaning , Facts, Information and Description

The Biot-Savart Law describes the magnetic field set up by a steadily flowing line current: the field produced by a current element is

where is the magnetic constant, I is the current and is the unit vector from the element to the field point. Hence, integrating, the field produced by current flowing in a loop is

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 aerodynamic theory. (The theory is closely parallel to that of magnetostatics; vorticity corresponds to current, and induced velocity to magnetic field strength.)

For an vortex line of infinite length, the induced velocity at a point is given by

v = Γ/(4πd)

where Γ is the strength of the vortex, and d is the perpendicular distance between the point and the vortex line. This is a limiting case of the formula for vortex segments of finite length:

v = Γ/(8πd) (cos(A) - cos(B))

where A and B are the (signed) angles between the line and the two ends of the segment.

See: Jean Baptiste Biot, Felix Savart, magnetism, vorticity

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