My textbook (high school level) derives an instance of Gauss's Law with Dielectric for the case in which the dielectric material fills the gap between a parallel-plate capacitor entirely.(adsbygoogle = window.adsbygoogle || []).push({});

So you get surface int (D dot Area-vector) = q, where D = (dielectric constant)(epsilon_0)(Electric field), and q is the free charge (on capacitor)

In the following example, the book shows how to compute the electric field inside a dielectric material between a parallel-plate capacitor, but the material in this case does not fill the entire gap. However, they utilize the version of Gauss's Law above. I guess the above version of Gauss's law holds as along as a portion of the dielectric material is inside the Gaussian surface used? After the derivation, the text did state that "this holds true generally and is the most general form of Gauss's Law."

btw, this is a high school text, so all e-fields, dielectric constants, etc are assumed to be uniform.

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# Gauss's Law with Dielectric

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