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How shall we apply Gauss's law for a space such that the volume enclosed by the Gaussian surface have 2 or more mediums with different dielectric constants, such that equal or more than two dielectrics pass through the Gaussian surface.

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If the dielectric has permittivity $\epsilon = \epsilon_r \epsilon_o$, where $\epsilon_r$ is the relative permittivity or dielectric constant of the dielectric and $\epsilon_o$ is the permittivity of free space, then $\iint_S \epsilon \vec E \cdot d\vec A = Q$ is the form of Gauss's law to used.
$\epsilon \vec E$ is called the displacement $\vec D$.

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    $\begingroup$ Doesn't the question mention multiple dielectrics in the question details? Why is this answer marked accepted? $\endgroup$ – Saprativ Ray Apr 21 '16 at 20:07
  • $\begingroup$ You can use different values of the relative permittivity when doing the surface integral depending on which medium that part of the area is immersed in. $\endgroup$ – Farcher Apr 21 '16 at 20:19
  • $\begingroup$ So, D is the same regardless of permittivity, so for example a sphere, with upper hemmisphere $\varepsilon_1$ and the lower hemisphere is $\varepsilon_2$, the gaussian will still be a sphere? $\endgroup$ – James Guana Apr 21 '16 at 20:46

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