A plane slab of thickness d has a uniform volume charge density . We have to find the magnitude of the electric field at all points in space both (a) inside and (b) outside the slab, in terms of x, the distance measured from the meridian plane of the slab.

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(a)

Plane slab of thickness d has a uniform volume charge density . By symmetry the field inside the slab and outside the slab will be perpendicular to the slab. The magnitude of the electric field at distance x on both sides of the meridian plane will also be equal. Let us consider a Gaussian surface of cross-sectional area A as shown in the figure.

Then, by applying the Gauss’ law we get

(b)

Now by considering a Gaussian surface that is symmetric with respect to the meridian but lies outside the slab and by applying the Gauss’ law, we find

Therefore,