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## Homework Statement

Uniform Slab: Consider an inﬁnite slab of charge with thickness 2a. We choose the origin inside the slab at an equal distance from both faces (so that the faces of the slab are at z = +a and z = −a). The charge density ρ inside the slab is uniform (i.e., ρ =const). Consider a point with coordinates (x,y,z). Using Gauss’ law, ﬁnd the electric ﬁeld

(a) when the point is inside the slab (−a < z < +a),

(b) and when the point is outside the slab (z > a or z < −a).

(c) Sketch the Ez vs z graph.

(d) If the density was not constant at its a function of z like ##ρ=Bz^2## then calculate the upper steps again.

## Homework Equations

Gauss Law

## The Attempt at a Solution

a) I took a cylinder Gaussian surface inside the slab forand from that I found ##E=\frac {ρz} {2ε_0}## .z is the height of the point that we choose from the origin.

b)I took a cylinder again and from that I found ##E=\frac {ρa} {2ε_0}##

c)The field will be constant cause ρ and a is constant also ##ε_0## so As z increases it inrease until a.And from that its constant.

d)Then Electric field will be ##E=\frac {Bz^3} {6ε_0}## for inside , ##E=\frac {Ba^3} {6ε_0}## for outside ?

Is these true ?

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