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This tag is for questions regarding to the boundary conditions (b.c.) which expresses the behaviour of a function on the boundary (border) of its area of definition. The choice of the b.c. is fundamental for the resolution of the computational problem: a bad imposition of b.c. may lead to the divergence of the solution or to the convergence to a wrong solution.
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Behavior of the electric field on boundary surfaces
You are using Gauss's Law. $\ Electric\ Flield's\ Flux= \frac{Q}{\epsilon_0}$
Calculate the flux through the 6 surfaces first.
When $\Delta x\rightarrow0$,
Then the contribution of flux coming from …