Key Equations

Definition of electric flux, for uniform electric field	$\text{Φ}=\overrightarrow{\text{E}}·\overrightarrow{\text{A}}\to EA\text{cos}\theta$
Electric flux through an open surface	$\text{Φ}={\displaystyle {\int }_S\overrightarrow{\text{E}}·\widehat{\text{n}}dA}={\displaystyle {\int }_S\overrightarrow{\text{E}}·d\overrightarrow{\text{A}}}$
Electric flux through a closed surface	$\text{Φ}={\displaystyle {\oint }_S\overrightarrow{\text{E}}·\widehat{\text{n}}dA}={\displaystyle {\oint }_S\overrightarrow{\text{E}}·d\overrightarrow{\text{A}}}$
Gauss’s law	$\text{Φ}={\displaystyle {\oint }_S\overrightarrow{\text{E}}·\widehat{\text{n}}dA=}\frac{q_{\text{enc}}}{{\epsilon }_0}$
Gauss’s Law for systems with symmetry	$\text{Φ}={\displaystyle {\oint }_S\overrightarrow{\text{E}}·\widehat{\text{n}}dA=E}{\displaystyle {\oint }_{S}dA}=EA=\frac{q_{\text{enc}}}{{\epsilon }_0}$
The magnitude of the electric field just outside the surface of a conductor	$E=\frac{\sigma }{{\epsilon }_0}$