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education/physics/PHYS2220/Gauss's Law.md
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@@ -11,4 +11,12 @@ $$ \Phi = EA$$
If the area is tilted relative to the field, then the strength of the field is reduced by a factor of $\cos \theta$, where $\theta$ is the angle between the electric field $\vec{E}$ and a vector $\vec{A}$ that's normal to the surface. This generalizes our flux equation to $\Phi = EA\cos\theta$ . If the area is tilted relative to the field, then the strength of the field is reduced by a factor of $\cos \theta$, where $\theta$ is the angle between the electric field $\vec{E}$ and a vector $\vec{A}$ that's normal to the surface. This generalizes our flux equation to $\Phi = EA\cos\theta$ .
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I don't understand what the below section 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:
$$ \Phi = \oint \vec{E} \cdot d\vec{A} \alpha q_{enclosed} $$
$$ \Phi = \oint \vec{E} \cdot d\vec{A} = \oint EdA \cos\theta$$
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