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# Illustration Electric flux and enclosed charge (1st Maxwell equation)

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The first Maxwell equation in integral form:$\oint_A \boldsymbol{E} ~\cdot \text{d}\boldsymbol{a} ~=~ \frac{Q}{\varepsilon_0}$connects the charge $$Q$$ trapped within the surface $$A$$ with the electric flux $$\oint_A \boldsymbol{E} ~\cdot \text{d}\boldsymbol{a}$$ through the surface $$A$$. The scalar product $$\boldsymbol{E} ~\cdot \text{d}\boldsymbol{a}$$ picks out only the portion of the electric field $$\boldsymbol{E}$$ parallel to the $$\text{d}\boldsymbol{a}$$ element. All other parts are eliminated in the scalar product.