notes/education/physics/PHYS2220/Gauss's Law.md

Flux

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.

While there's nothing directly flowing in an electric field, the term flux is used to describe the total strength of a field.

In the simplest case with a uniform field of magnitude E perpendicular to an area A, the flux is described as follows:

\Phi = EA

• E refers to the amplitude
• A refers to the area

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: 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} \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

For a closed sphere, the equation becomes:

\Phi = E(4\pi r^2)

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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