Homework Help: Gauss' law help please.

For this problem I am giving the following:

An infinite slab of charge parallel to the yz plane whose density is given by:

p(x)= t, -b<x<b;
0, |x|>b;

Where t and b are constants.

And I am to find the electric field.

I am pretty confused on how to do this problem. I know that the electric field is in the x direction, and that is also where the normal to the surface is directed. So I thought it would be:

[tex]2 v E =\frac{q}{\epsilon}[/tex] where the q = [tex]\frac{p}{v}[/tex]

Where v is the volume, similar to how you do an infinite sheet but I don't get the right answer. But then q would be 0 for outside of b and that is not right so I guess my method is completely wrong.

 

Thanks, but I think I need to do it a different way. We are using Gauss' law in its basic form of [tex]\int\int_s E . n ds=\frac{q}{\epsilon}[/tex] I guess I am confused because for a infinite thin sheet you get [tex]\frac{\sigma}{2 \epsilon}[/tex] and it would seem outside of the slab this is what the field would be, but it isn't, it is [tex]\frac{\rho b}{\epsilon}[/tex]

By looking on another website I think to have found it, I did the following integral:

[tex]\int_b^b \rho dx[/tex] which seems to give me the right answer but I don't really understand it. The bottom limit is -b but I couldn't get latex to do it right

 

Ya, I figured it out it just took me a while to remember all the stuff I learned last year. It wasn't that I thought what you had wasn't Gauss' law, I just wasn't sure how to put it into the form I needed. Thanks for the help.