Gauss' Law Video Lessons

Concept

# Problem: 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 Eout, the magnitude of the electric field outside the slab? As implied by the fact that Eout 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 ε0.B. What is Ein, the magnitude of the electric field inside the slab as a function of x? Express your answer in terms of x, ρ, and ε0.

###### FREE Expert Solution

Gauss's law:

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

A.

It is given that Eout is not a function of x.

This implies that the magnitude, Eout is constat everywhere outside the slab and not just at the surface.

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###### Problem Details

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 Eout, the magnitude of the electric field outside the slab? As implied by the fact that Eout 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 ε0.

B. What is Ein, the magnitude of the electric field inside the slab as a function of x? Express your answer in terms of x, ρ, and ε0.