OpenStax University Physics/E&M/Gauss's Law

$ℰ\mathrm{\&}ℳ$ (Vol. 2):Template:Spaces 5:Electric Charges and FieldsTemplate:Spaces 6:Gauss's LawTemplate:Spaces 7:Electric PotentialTemplate:Spaces 8:CapacitanceTemplate:Spaces 9:Current and ResistanceTemplate:Spaces 10:Direct-Current CircuitsTemplate:Spaces 11:Magnetic Forces and FieldsTemplate:Spaces 12:Sources of Magnetic FieldsTemplate:Spaces 13:Electromagnetic InductionTemplate:Spaces 14:InductanceTemplate:Spaces 15:Alternating-Current CircuitsTemplate:Spaces 16:Electromagnetic Waves

Chapter 6

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For quiz at QB/d_cp2.6

Template:Colbegin $\mathrm{\Phi }=\overrightarrow{E}\cdot \overrightarrow{A}$ $\to \int \overrightarrow{E}\cdot d\overrightarrow{A}=\int \overrightarrow{E}\cdot \hat{n}dA$ = electric flux

$q_{enclosed}={\epsilon }_0\oint \overrightarrow{E}\cdot d\overrightarrow{A}$

$d\text{Vol}=dxdydz=r^{2}drdA$ where $dA=r^{2}d\varphi d\theta$

$A_{\text{sphere}}=r^2\underset{0}{\overset{\pi }{\int }}\sin \theta d\theta \underset{0}{\overset{2\pi }{\int }}d\varphi =4\pi r^2$ Template:Colend