# Illustration Electric flux - scalar product of surface orthogonal vector and E-field

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For the First Maxwell equation you can use any closed volume, like in this case a cube volume. The electric flux $$\Phi$$ through the infinitesimal surface element of the cube is defined as the scalar product between the electric field vector $$\boldsymbol{E}$$ at the considered surface point and the surface orthogonal vector $$\text{d}\boldsymbol{a}$$. $$\text{d}\boldsymbol{a}$$ is orthogonal to the considered surface element and its magnitude represents the area of the surface element:$\text{d}\Phi = \boldsymbol{E} \cdot \text{d}\boldsymbol{a}$

The electric field vector $$\boldsymbol{E}$$ can be divided into a component $$\boldsymbol{E}_{\perp}$$ orthogonal to $$\text{d}\boldsymbol{a}$$ and into a component $$\boldsymbol{E}_{||}$$ parallel to $$\text{d}\boldsymbol{a}$$. The scalar product with the orthogonal component is always zero.