Uniform volume density between two planes - Corrected Exercises Gauss Theorem

 

Consider two infinite planes x = - a and x = a. The space between the two planes has a volume density of uniform and constant ρ loads. For x> a and x <- a, it reigns on vacuum .

1. Show that at any point of space, the electrostatic field of this distribution can be written .
2. Expressing Ex for the different parts of space and plot the Ex a function of x.
3. Determine for each region the potential V (x) adopting V (0) = 0. Draw the graph of V (x) in terms of x.
4. It is assumed that a approaches 0 and that the multiplication  ρa remains finite. Set an areal density limit load and look for Ex  on a classic result.

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