Advanced Placement Physics C: Electricity and Magnetism with calculus applications.
Electric flux measures how much electric field passes through a surface. Think of it like counting the number of electric field lines crossing a surface.
Gauss’s Law relates electric flux through a closed surface to the charge inside:
\[ \oint \vec{E} \cdot d\vec{A} = \frac{q_{in}}{\varepsilon_0} \] where \( \vec{E} \) is the electric field, \( d\vec{A} \) is a small area on the surface, \( q_{in} \) is the enclosed charge, and \( \varepsilon_0 \) is the permittivity of free space.
Gauss’s Law is especially useful when dealing with symmetrical charge distributions (spheres, cylinders, planes), allowing you to easily find electric fields.
Gauss’s Law is why the electric field inside a metal conductor is zero—charges redistribute on the surface.
Finding the electric field inside and outside a charged sphere.
Explaining why static charge resides only on the surfaces of conductors.
Gauss’s Law connects electric fields and charge, making tough field calculations easier in symmetric situations.