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Electric field near a charged slab

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A planar slab of thickness of 4.00 cm has a uniform volume charge density of 1.20×10-2 C/ m3. Find the magnitude of the electric field at all points in space both inside and outside the slab, in terms of x, the distance measured from the central plane of the slab. What is the field for x = 1.00 cm? What is the field for x = 8.00 cm?

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Inside the slab, the electric field must be perpendicular to the central plane (which is parallel to the slab and divides it in two equal parts). To see this, consider rotating the slab about a line perpendicular to the central plane. The slab, after being rotated looks the same as before (we are assuming that the slab is infinite in the two directions parallel to the central plane), the charge densities are still the same as before, so the field must be the same. Since, in general, the field must rotate with the slab if the slab is rotated, this means that the field must be parallel to the rotation axis which is perpendicular to the central plane.

Let's define the coordinate x such that x = 0 on the ...

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