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If the two plates are made of conducting material, there is nothing preventing charges from flowing as close as possible to each other, which, in this case, means toward the edge of each plate closest to the other, right next to the insulating layer. If we now suppose the layer to be thin (dimension $d$) with respect to the plates' sides $L = 10\; cm$), ...


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Normally, physical problems are solved by the integral form of Gauss's law $$ \iint_S\,\mathbf{D}\bullet d\mathbf{s} = \rho $$ and the application of Gaussian Surfaces if the geometry of the problem allows. This quickly lets you work with discontinuities of the medium, adjusting the limits of integration. The differential form, fits differentials set ...


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Any inverse square law can be substituted by a Gauss law. In Gravitation, gravitational field $$E_{g}(R)=\frac{GM}{R^{2}}$$ Think of a sphere of Radius $R$ around the object of mass $M$ (This can be generalized to any shape). This gravitational flux coming out of it is $$\phi_{g}= E_{R}\times4\pi R^{2}=4\pi GM$$ So the gauss law will read as ...



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