What Does 'a' Represent in a Non-Constant Charge Density Equation?

[industry86]

an "infinite" sheet with a thickness has a uniform density charge. however, my teacher gave it in rho=az^2. I know what rho is, and I know what z is. What is 'a'? He's used it in an example or two, but never thought to ask what it means and if it's consistent for all distances of the electric field and whatnot...
If I could just know this, then I think my life would be much easier and I think I could figure out this problem. I've looked online and throughout my book but I cannot find it's reference anywhere. I've found it one place in this forum, but it wasn't explained because it seemed everybody already knew.
Thanks for any help.

 

[Chi Meson]

Hmm. I don't recognize this particular formula. So, what is rho here? Is is volumetric charge density? Is "z" the position through the thickness? If this is the case then the fomula gives the charge density as a function of distance as you move through the thickness of the plate. Then "a" would be some constant particular to any given situation. And if this is so, then it is not a uniform charge density.

 

[industry86]

Hmm. I don't recognize this particular formula. So, what is rho here? Is is volumetric charge density? Is "z" the position through the thickness? If this is the case then the fomula gives the charge density as a function of distance as you move through the thickness of the plate. Then "a" would be some constant particular to any given situation. And if this is so, then it is not a uniform charge density.

well, in the particular instance of the problem i have, rho is in reference to volumetric charge density, z is the distance from the center of the plate. i have seen it used in either a radius or linear capacity. and I know it's dimensionally C/m^? since I've seen the m with powers of 4 or 5. So I'm at a loss.

 

[DaMastaofFisix]

Hmm, seems like we have a little issue here. If the volume density is really what's given, the it sure isn't constnat, not one bit. This question Is nothing more than an extension of gauses law. When calculating the flux through a gaissian surface, most of the time the density is constant, and thus makes the calculation of the Qnet much easier. But if the density is a function of the distance, then that's got to be taken into consideration, as is the case for this problem. Recall that the flux through a gaussian surface is the CLOSED integral of E dA cos(theita)= Qenclosed/epsilon. Assuming your given a thickness z, you can create your gaussian surface and your limits of integration. AS far as I know, that seems to be the only way to solve this puppy, algebra just won't do. Give it a shot and see wha you can do with it.