Physics 7B - Chapter 22: Gauss's Law

Flux

refers to the electric field passing through a given area perpendicular to the electric field lines

Flux through area

\Phi_{E}=\overrightarrow{E}\cdot\overrightarrow{A}=EA\cos\left(\theta\right) }$$

Flux through enclosed surface

\int_{}^{}\!\overrightarrow{E}\,\cdot d\overrightarrow{A}

Net flux from external charges

Always equal to zero

Gauss’s Law

Gives relationship between flux through a closed surface and net charge enclosed within the surface.

\int\overrightarrow{E}\cdot\overrightarrow{dA}=\frac{Q_{encl}}{\varepsilon_0}

Electric Field at point R from a Conductive Sphere

\frac{1}{4\pi\varepsilon_0}\cdot\frac{Q}{r^2} (same formula as for point charge because E is zero for points inside surface)

Electric Field at point R from Wire/Line of Charge

E=\frac{\lambda}{2\pi R\varepsilon_0}

Electric field just outside the surface of a conductor

E=\frac{\sigma}{\varepsilon_0}

Enclosed surfaces for Gauss’s Law

Circle, Sphere, Cylinder, Pillbox