Biot-Savart law

The Biot-Savart Law describes the magnetic field set up by a steady current density.

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In particular, if one defines a current element dmathbf{l}, then the field element produced is

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: dmathbf{B} = K_m rac{I dmathbf{l} imes mathbf{hat r}}{r^2} .

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As a result, field produced by a current is:

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: mathbf B = K_m I int rac{dmathbf l imes mathbf{hat r}}{r^2}

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where

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:K_m = rac{mu_0}{4pi} is the magnetic constant

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:I is the current, measured in amperes

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:mathbf{hat r} is the unit displacement vector from the element to the field point,

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:and the integral is over the current distribution.

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In the special case of a charged point particle q moving at a constant velocity mathbf{v}, then the equation above reduces to a magnetic field of the form:

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: mathbf{B} = K_m rac{ q mathbf{v} imes mathbf{r}}{r^3}

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The Biot-Savart law is fundamental to magnetostatics just as Coulomb's law is to electrostatics. It is consistent with Ampère's law, much as Gauss' law is consistent with Coulomb's law.

Related Topics:
Magnetostatics - Coulomb's law - Electrostatics - Ampère's law - Gauss' law

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