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Physics LibreTexts

15.2: Maxwell's First Equation

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Maxwell's first equation, which describes the electrostatic field, is derived immediately from Gauss's theorem, which in turn is a consequence of Coulomb's inverse square law. Gauss's theorem states that the surface integral of the electrostatic field D over a closed surface is equal to the charge enclosed by that surface. That is

surfaceDdσ=volumeρdv

Here ρ is the charge per unit volume.

But the surface integral of a vector field over a closed surface is equal to the volume integral of its divergence, and therefore

surfacedivDdv=volumeρdv

Therefore

divD=ρ,

or, in the nabla notation,

D=ρ.

This is the first of Maxwell's equations.


This page titled 15.2: Maxwell's First Equation is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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