Flux of the Electric Field

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Section 13.1 Flux of the Electric Field

The most natural direction associated with a surface is the direction perpendicular to it. Therefore, the natural integral to compute over a surface adds up the normal component of $\EE\text{.}$ This is called the flux of $\EE$ through the given surface (in the given direction):

\begin{gather*} \hbox{flux} = \int \EE \cdot \nn \, dA = \int \EE \cdot d\AA . \end{gather*}

Be warned that some authors use two integral signs rather than one, and other letters, such as $S$ or $\sigma\text{,}$ are often used in place of $A\text{.}$