Definition:Electric Flux

Definition
Let $\delta \mathbf S$ be an element of a vector area in an electric field whose strength is $\mathbf E$.

The electric flux through $\delta \mathbf S$ is defined as the dot product of $\mathbf E$ with $\delta \mathbf S$:
 * $\mathbf E \cdot \delta \mathbf S$

That is, by definition of dot product:
 * the magnitude $E$ of $\mathbf E$

multiplied by:
 * the projection of $\delta \mathbf S$ onto $\mathbf E$

That is:
 * $E \rdelta S \cos \psi$

where $\psi$ is the angle made by $\delta \mathbf S$ with $\mathbf E$.