As shown in the right figure, an infinite slab of charge of thickness 2a is cent

Question

As shown in the right figure, an infinite slab of charge of thickness 2a is centered in xy-plane.        The charge density is ? = ?0(1 - |z|/a).        Find the electric field strengths (16 points)         

As shown in the right figure, an infinite slab of charge of thickness 2a is centered in xy-plane. The charge density is ? = ?0(1 - |z|/a). Find the electric field strengths inside the slab of charge. outside the slab of charge. [Draw and show the Gauss surface you are using whenever you apply Gauss' law, and explain why you choose it.]

Explanation / Answer

part 1

draw a box enclosing a region inside the slab from -z to z

flux through the 2 surfaces = E x area = charge inside

E x 2 x length of box = (rhonot x length of box x (2z)/a) / epsilonnot

E = (rhonot x z/a) /epsilonnot

part 2

draw a box enclosing whole of the slab and part of the region outside the slab from -z to z

flux through the 2 surfaces = E x area = charge inside

E x 2 x length of box = (rhonot x length of box x (2a)/a) / epsilonnot

E = rhonot / epsilonnot

the surfaces have been taken so because of the symmetry in the problem along the z axis

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