Using Gauss Law to Solve a Planar Slab of Charge Problem

[brad sue]

Hey, I need help to use the Gauss law in this problem:

We have A planar slab of charge with a charge density ρ_v=ρ_vosin(2*pi/(2*a)),for -a<x<a
the thickness of the stab is 2*a.
the horizontal y-axis passes through the middle of the stab.
the x-axis is vertical
a) Find the electric field vector in the region -a<x<a.

I know I need to use the Gauss law.
But I have some problems to establish the integral.
What surface should I take?

I tried the cylinder as surface of integration.
I got:
FLUX=2(pi)x*L*D_x=Q_enclosed
Then I am stuck.
The Q_enclosed integration give me some problem.
Please can someone help me to establish the Gauss law to solve the problem?

 

[Saketh]

Tactical use of Gaussian surfaces is a skill one acquires after suffering through many Gauss's law problems. So don't fret if you don't get it immediately.

In this case, since the planar charge distribution has uniform charge density (ρv=ρvosin(2*pi/(2*a)) is a constant), the electric field at x = 0 would be zero, because of symmetry. Convince yourself that this is true. Based on this, figure out where to put your Gaussian surface.

When you say I tried "the cylinder", success often depends on where you put its faces.

The enclosed charge is simple enough to determine -- just multiply the charge density by the volume enclosed by the Gaussian surface. (Or did you mean to give a charge distribution that depends on x?)