In all the coax examples it should be ln(b/a) instead of ln(a/b), which would make the capacitance negative, according to the notation of 'a' and 'b' in the illustrations.
I am looking for a proof that the treatment of the inhomogeneous dielectrics via individual homogeneous plate capacitors is valid for more complex structures. I can do the proof for simple series or parallel inhomogeneities, like in your video, but am stumped to derive it when the dielectric is inhomogeneous in all three spatial dimensions. Do you maybe have a ressource that deals with this in more detail?
I don't know of any resource that does this. In general, I think this is an approximation. Treating the inhomogeneities as a network of series and parallel connections ignores the fringing effects of the fields that tends to redistribute the energy a little bit.
I used MATLAB, but I have also used Octave in the past. Both work well. If you want to see more about how I use MATLAB (or Octave) to do this, see Lectures 6b to 7e in the following course: empossible.net/academics/emp4301_5301/
Professor Rumpf, when we apply Gauss' law to coax cable why does the unit area look like that?Should the third component of the sum be ro*d(ro)*d(fi)? Thank you
If d(rho) was a term, that would imply integrating in the rho direction. Gauss' law is applied over a surface enclosing the charge. This is a cylindrical area that extends in the directions of phi and z. The rho direction would cut through the charges.
In all the coax examples it should be ln(b/a) instead of ln(a/b), which would make the capacitance negative, according to the notation of 'a' and 'b' in the illustrations.
I am looking for a proof that the treatment of the inhomogeneous dielectrics via individual homogeneous plate capacitors is valid for more complex structures. I can do the proof for simple series or parallel inhomogeneities, like in your video, but am stumped to derive it when the dielectric is inhomogeneous in all three spatial dimensions. Do you maybe have a ressource that deals with this in more detail?
I don't know of any resource that does this. In general, I think this is an approximation. Treating the inhomogeneities as a network of series and parallel connections ignores the fringing effects of the fields that tends to redistribute the energy a little bit.
Great video ;)
Sir, in the supplement information, where the model of parallel plate capacitor had done, can you tell me which software was used?MATLAB?
I used MATLAB, but I have also used Octave in the past. Both work well. If you want to see more about how I use MATLAB (or Octave) to do this, see Lectures 6b to 7e in the following course:
empossible.net/academics/emp4301_5301/
Professor Rumpf, when we apply Gauss' law to coax cable why does the unit area look like that?Should the third component of the sum be ro*d(ro)*d(fi)? Thank you
If d(rho) was a term, that would imply integrating in the rho direction. Gauss' law is applied over a surface enclosing the charge. This is a cylindrical area that extends in the directions of phi and z. The rho direction would cut through the charges.
I got used to generically applying Gauss' Law and it caught up with me.
Thank you for your lectures, they make the "first step" easy!
THANK YOU.