Recent content by approx12

1. Capacitance of a parallel-plate Capacitor with non uniform dielectric

Thanks to everyone for the discussion and the help with this problem, I learned quite a bit by that. Gonna be extra careful on the next problem. I dont't want to be too annoying but I have two last questions: 1) In your first equation here, did you pull the constant ##4\pi## from...
2. Capacitance of a parallel-plate Capacitor with non uniform dielectric

Thank you, I didn't thought about it that way, that makes good sense! Already learned something, thanks. Would it possible if you could also give me a small hint on a starting point on how to get the ##\vec{E}## or ##\vec{D}##-Field mathmatically? What "Ansatz" should I try? I can't seem to...
3. Capacitance of a parallel-plate Capacitor with non uniform dielectric

Thanks too for taking the time to comment! I'm trying to think about this (that ##D## is dependent on ##\epsilon(r)##) but I can't seem to get to the point to see it. The maxwell equation says: $$\vec{\nabla}\cdot \vec{D} = 4\pi\rho_f$$ But since we are in a dielectric with the only free...
4. Capacitance of a parallel-plate Capacitor with non uniform dielectric

Thanks for taking the time to comment on my problem! So looks like I was on the wrong path. If voltage drop is constant, then my Electric field ##\vec{E}## should not depend on the radius ##r## right? I dont't know what that would say about my free surface charge though. Shouldn't it per...
5. Capacitance of a parallel-plate Capacitor with non uniform dielectric

Hey guys! I'm having trouble with the solution that I arrived at. Through boundary conditions I'm able to determine ##\vec{D}## as $$\vec{D}=-\frac{4Q}{R_0^2}\hat{e_z}$$ (In CGS units) Trough that I'm able to get the electric field as $$\vec{E}=-\frac{1}{\epsilon(r)}\frac{4Q}{R_0^2}\hat{e_z}$$...
6. Calculating work and heat transfer in this Carnot process

Hey guys! This is problem from Callens Thermodynamics textbook and I'm stuck with it. My goal was to get a expression for the entropy ##S## which is dependent on ##T## so I can move into the ##T-S##-plane to do my calculations: I startet by expressing the fundamental equation as a function of...
7. Writing the charge density in the form of the Dirac delta function

Oh, thank you, I was not familiar with this general formula. Are there maybe any references to it in some books or online so I can look it up? But to the problem: So, it looks like the charge density reduces in my case to: $$\rho=\sigma\delta(z)$$ Which, I think, refers to a surface charge...
8. Writing the charge density in the form of the Dirac delta function

Hi, thanks for taking the time to reply! I think I'm not quite sure what you mean with ##\Phi(\vec{x})=0##, do you mean the electric potential or some plane equation (that would be ##z=0## for the ##xy##-plane I guess). I also thought about writing the charge density in combination with the...