Recent content by Madoro

oh, I see my error, the field is actually discomposed as \vec{E}=E\vec{r}+E\vec{z}, where I have named E_r=E(r,z)\vec{r} and E_z=E(r,z)\vec{z}, but I think I'm getting lost with the nomenclature, because then I only know Er at the discharge point, when z=0: E_r(r,0)=\frac{U}{rLog(R_i/R_{tip})}...

Yes, now I see, since \rho = \rho(r,z), \frac{\partial E_z}{\partial z}=f(r,z). Then I don´t know if it is a conceptual mistake from me, but I was thinking that since \vec{E}=E_r\vec{r}+E_z\vec{z}, each component was depending on each variable, Er=E(r) and Ez=E(z), and therefore the...

oops, sorry about the confussion, subscripts denote components of the electrical field: \vec{E}=E_r\vec{r}+E_z\vec{z}, neglecting the variation in the azimuthal direction. The Poisson equation shown is the result of operating in cylindrical components: \frac{1}{r}\frac{\partial (r...

Hi Haruspex, first of all thank you very much for your help. Your suggestion of separating variables gave me the idea of instead of separating Ez, which is supposed to only depend on z, separate \rho(r,z)=R(r)Z(z) Then, the Poisson eq: dE=\frac{RZ}{\epsilon_0}dz and the eq in \rho...

I have an electrostatics problem (shown here: https://www.physicsforums.com/showthread.php?t=654877) which leads to the following system of differential equations: \frac{\partial E_z}{\partial z}=\frac{\rho}{\epsilon_0} (1) Z_i E_r \frac{\partial \rho}{\partial r}+(u_g+ Z_i E_z)...

Second attempt: I divide the problem in two parts, first inside the inner cylinder and then in the bigger one. I'll begin in the inner one where discharge is started I suppose a radial discharge from the tip to the walls: E_r=\frac{U}{r Log(R_i/R_{tip})} being U the applied voltage and...

Homework Statement Hello, I have an experimental problem that I don´t know how to express theoretically. It consists on a tip at high voltage inside an earthed cylinder, where a discharge is produced. The discharge is radial, since is the shortest distance to the wall, and produces ions, which...