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What is the correct formula for electric permittivity?

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If you are looking for a formula for $\epsilon_0$ (vacuum permittivity), you will not find it, because $\epsilon_0$ is a constant. $$\epsilon_0=8.854187817\times 10^{−12} \frac{F}{m}$$ In other hand, permitivity $\epsilon$ is defined as follows $$\epsilon=(1+\chi_e)\epsilon_0$$ Where $\chi_e$ is called the electric susceptibility, and is defined with $$\mathbf{P}=\chi_{e}\epsilon_{0}\mathbf{E}$$ Where $\mathbf{P}$ is the polarization vector.

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