Biot–Savart law

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The Biot–Savart law (pronounced /ˈbiːoʊ səˈvɑr/ or /ˈbjoʊ səˈvɑr/)[1] is an equation in electromagnetism that describes the magnetic field B generated by an electric current. The vector field B depends on the magnitude, direction, length, and proximity of the electric current, and also on a fundamental constant called the magnetic constant. The law is valid in the magnetostatic approximation, and results in a B field consistent with both Ampère's circuital law and Gauss's law for magnetism.[2]

Contents

Introduction

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

or, equivalently,

where

The symbols in boldface denote vector quantities.

To apply the equation, you choose a point in space at which you want to compute the magnetic field. Holding that point fixed, you integrate over the path of the current(s) to find the total magnetic field at that point. The application of this law implicitly relies on the superposition principle for magnetic fields, i.e. the fact that the magnetic field is a vector sum of the field created by each infinitesimal section of the wire individually.[3]