Gauss's law:

$\overline{){\mathbf{\varphi}}{\mathbf{=}}\frac{\mathbf{Q}}{{\mathbf{\epsilon}}_{\mathbf{0}}}}$

**A.**

It is given that E_{out }is not a function of x.

This implies that the magnitude, E_{out }is constat everywhere outside the slab and not just at the surface.

A slab of insulating material of uniform thickness d, lying between -d/2 to +d/2 along the x axis, extends infinitely in the y and z directions. The slab has a uniform charge density ρ. The electric field is zero in the middle of the slab, at x = 0.

A. What is E_{out}, the magnitude of the electric field outside the slab? As implied by the fact that E_{out} is not given as a function of x this magnitude is constant everywhere outside the slab, not just at the surface. Express your answer in terms of d, ρ, and ε_{0}.

B. What is E_{in}, the magnitude of the electric field inside the slab as a function of x? Express your answer in terms of x, ρ, and ε_{0}.

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