Biot-Savart law: Difference between revisions

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In [[physics]], more particularly in [[electrodynamics]], the law first formulated by [[Jean-Baptiste Biot]] and [[Felix Savart|Félix Savart]] <ref>J.-B. Biot and F. Savart, ''Note sur le Magnétisme de la pile de Volta,'' Annales Chim. Phys. vol. '''15''', pp. 222-223 (1820)</ref> describes the magnetic field caused by a direct electric current in a wire. Biot and Savart interpreted their measurements by an integral relation. [[Laplace]] gave a differential form of their result, which now often is also referred to  as the Biot-Savart law, or sometimes as the Biot-Savart-Laplace law. By integrating Laplace's equation over an infinitely long wire, the original integral form of Biot and Savart is obtained.
#REDIRECT [[Biot–Savart law]]
[[Image:Laplace magnetic.png|right|thumb|250px|Magnetic field d'''B''' at point '''r''' due to  infinitesimal piece d'''s''' (red) of wire (blue) transporting electric current ''i''. ]]
==Laplace's formula==
The infinitesimal [[magnetic induction]] d'''B''' at point '''r''' is given by the following formula due to Laplace,
:<math>
d\vec{\mathbf{B}} = k \frac{i d\vec{\mathbf{s}} \times \vec{\mathbf{r}}} {|\vec{\mathbf{r}}|^3},
</math>
where the magnetic induction is given as a [[vector product]], i.e., is perpendicular to the plane spanned by d'''s''' and '''r'''.  The constant ''k'' depends on the units chosen. In rationalized SI units ''k'' is  the [[magnetic constant]] (vacuum permeability) &mu;<sub>0</sub> = 4&pi; &times;10<sup>&minus;7</sup> N/A<sup>2</sup> (newton divided by ampere squared). If we think of the fact that the vector '''r''' has dimension length, we see that this equation is an [[Inverse-square_law|inverse distance squared law]].
 
'''(To be continued)'''
==References==
<references />

Latest revision as of 13:18, 22 April 2011

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