Electric Field and Potential for an infinite slab with uniform charge density ρ

PROBLEM:  Consider an infinite slab parallel to  the x-z plane  (normal to the y axis) of uniform charge density ρ and thickness 2a, as shown:


Find the Electric Field and Potential everywhere.

(a)  First, present your arguments for treating this problem as one dimensional.

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We wish to derive the E field, (OverVector[E])(y), at all values of y.

(b) Start with E outside the slab.

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(c) Now find E inside the slab.

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(d) Plot the magnitude of EE[y] for both inside and outside the slab.

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(e) Comment on this plot

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(f) Now generate a 2D Vector Plot of the E-Field both inside and outside of the slab of charge (assume a positive ρ).

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(g) Comment on this vector plot

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(h) Derive and plot the 1D Electric Potential vs. y for the above E Field.

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(i)Comment on this result (the plot).

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