- #1
meteorologist1
- 98
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Please consider this problem:
A plastic slab of thickness t has a uniform free charge density, +rho, embedded inside, and also one surface has a surface charge of -sigma. Find the electric fields here and sketch as a function of distance from one surface. Also find the potential as a function of distance, sketch results. [Ignore issues of dielectric polarizability, the function of the plastic is simply to fix the charges in place]
Here is what I did: I draw a Gaussian pillbox with area A. Only the top and bottom caps contribute where E and dA are parallel. The charge enclosed is: (rho)(A)(t) + (-sigma)(A) = A((rho)(t) - sigma)
By Gauss's Law, we have: 2EA = [A((rho)(t) - sigma)] / epsilon, so therefore, E = ((rho)(t) - sigma) / 2epsilon
I'm not sure what I did wrong here since the question asks to plot E as a function of r. In my case I would have a constant line. What did I do wrong? Thanks.
A plastic slab of thickness t has a uniform free charge density, +rho, embedded inside, and also one surface has a surface charge of -sigma. Find the electric fields here and sketch as a function of distance from one surface. Also find the potential as a function of distance, sketch results. [Ignore issues of dielectric polarizability, the function of the plastic is simply to fix the charges in place]
Here is what I did: I draw a Gaussian pillbox with area A. Only the top and bottom caps contribute where E and dA are parallel. The charge enclosed is: (rho)(A)(t) + (-sigma)(A) = A((rho)(t) - sigma)
By Gauss's Law, we have: 2EA = [A((rho)(t) - sigma)] / epsilon, so therefore, E = ((rho)(t) - sigma) / 2epsilon
I'm not sure what I did wrong here since the question asks to plot E as a function of r. In my case I would have a constant line. What did I do wrong? Thanks.