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education/physics/PHYS2220/Gauss's Law.md
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@@ -13,10 +13,12 @@ If the area is tilted relative to the field, then the strength of the field is r
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I don't understand what the below section means, but copying it for posterity: I don't understand what the below section means, but copying it for posterity:
The electric flux through any closed surface is proportional to the net charge enclosed by that surface. This would be written mathematically as: The electric flux through any closed surface is proportional to the net charge enclosed by that surface. This would be written mathematically as:
$$ \Phi = \oint \vec{E} \cdot d\vec{A} \alpha q_{enclosed} $$ $$ \Phi = \oint \vec{E} \cdot d\vec{A} \propto q_{enclosed} $$
> interjection: $\propto$ means "is proportional to", and $\oint dA$ can *possibly* be treated as the area of the surface.
$$ \Phi = \oint \vec{E} \cdot d\vec{A} = \oint EdA \cos\theta$$ $$ \Phi = \oint \vec{E} \cdot d\vec{A} = \oint EdA \cos\theta$$
For a closed sphere, the equation becomes:
$$ \Phi = E(4\pi r^2) $$
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