26 lines
1.4 KiB
Markdown
26 lines
1.4 KiB
Markdown
# Flux
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Flux refers to a flow of matter or energy. Examples include water through a pipe, blood through veins, or air over an airplane's wing.
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While there's nothing directly *flowing* in an electric field, the term flux is used to describe the total strength of a field.
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In the simplest case with a uniform field of magnitude $E$ perpendicular to an area $A$, the flux is described as follows:
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$$ \Phi = EA$$
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- $E$ refers to the amplitude
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- $A$ refers to the area
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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 means, but copying it for posterity:
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The electric flux through any closed surface is proportional to the net charge enclosed by that surface. This would be written mathematically as:
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$$ \Phi = \oint \vec{E} \cdot d\vec{A} \propto q_{enclosed} $$
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> interjection: $\propto$ means "is proportional to", and $\oint dA$ can *possibly* be treated as the area of the surface.
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$$ \Phi = \oint \vec{E} \cdot d\vec{A} = \oint EdA \cos\theta$$
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For a closed sphere, the equation becomes:
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$$ \Phi = E(4\pi r^2) $$
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Before proceeding, we introduce the so-called permittivity constant $\in_0$, defined as $\in_0 = 1/4 \pi k$, where $k$ is the Coulomb constant.
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