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\begin{aligned} \displaystyle \Phi_\mathrm{E} = \oiintiint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \overline{\varepsilon}_0 qQ \end{aligned} |
where
is a closed Gaussian surfaceMathinline body \displaystyle S
is the electric field (“electric force”, i.e., force per charge)Mathinline body \displaystyle \mathbf{E}
is an infinitessimal surface normal area vector on surfaceMathinline body \mathrm{d}\mathbf{A} Mathinline body S
is the total electric charge (“quantity of electricity”) contained within the surfaceMathinline body \displaystyle Q
is the vacuum “elastivity” (reciprocal of vacuum “capacitivity” also known as vacuum permittivity)Mathinline body \displaystyle \overline{\varepsilon}_0 = \varepsilon_0^{-1}
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