Gauss' law (electrostatics): Difference between revisions
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\iint_{\mathrm{closed}\atop\mathrm{surface}} \mathbf{E}\cdot d \mathbf{S} =\frac{Q_\mathrm{tot}}{\epsilon_0}. | \iint_{\mathrm{closed}\atop\mathrm{surface}} \mathbf{E}\cdot d \mathbf{S} =\frac{Q_\mathrm{tot}}{\epsilon_0}. | ||
</math> | </math> | ||
Here d'''S''' is an vector with length d''S'', the area of an infinitesimal surface element, and direction perpendicular to the surface element d''S''. The vector '''E''' is the electric field at the position d'''S''', the dot indicates | Here d'''S''' is an vector with length d''S'', the area of an infinitesimal surface element, and direction perpendicular to the surface element d''S''. The vector '''E''' is the electric field at the position d'''S''', the dot indicates a [[dot product]] between the vectors '''E''' and d'''S'''. The double integral is over a closed surface that envelops a total electric charge ''Q''<sub>tot</sub>. The constant ε<sub>0</sub> is the [[electric constant]]. The law is called after the German mathematician [[Carl Friedrich Gauss]]. | ||
[[Category: CZ Live]] | [[Category: CZ Live]] | ||
[[Category: Physics Workgroup]] | [[Category: Physics Workgroup]] | ||
Revision as of 17:20, 28 March 2008
In physics, more specifically in electromagnetism, Gauss' law is a theorem concerning a surface integral of an electric field. In vacuum it takes the form (in SI units):
Here dS is an vector with length dS, the area of an infinitesimal surface element, and direction perpendicular to the surface element dS. The vector E is the electric field at the position dS, the dot indicates a dot product between the vectors E and dS. The double integral is over a closed surface that envelops a total electric charge Qtot. The constant ε0 is the electric constant. The law is called after the German mathematician Carl Friedrich Gauss.