Gauss law of electricity | Electrostatics | Physics | Khan Academy

Ultimate Gauss' Law review

<aside> 🐶 $\oiint s \overrightarrow{E} \cdot d \overrightarrow{A} = \frac{Q{enc}}{\epsilon _0}$ The electric flux through any closed surface is equal to the charge within that area

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• The flux of $\overrightarrow{E}$ over a closed surface $S$ is equal to the total charge (with their algebraic sign) enclosed in surface $S$ divided by free space permittivity $(\epsilon _0)$
  • Assume that charges reside inside the vacuum
  • No electric charges inside a perfect metal (no point defects)
  • Gauss’ Law is a surface integral, voltage is a line integral
• Pick a surface where the electric field is constant along that area, so you can “pull the electric field out of the integral”

Spherical Symmetry

Cylindrical Symmetry

Planar Symmetry

Flux of Electric Field

Area as a Vector & Open/Closed Surfaces

Evaluating a Double Integral

Charge Densities

Calculating $\vec{E}$ of a point charge at the distance $r$ from the point charge

First Shell Theorem

Second Shell Theorem

$\vec E$ for a uniform (non conducting) sheet of charge

$\vec E$ for a uniform line of charges, $\gamma$, $[C /m]$

$\vec E$ for a uniformly charged conducting plate