I have a coaxial cable with internal conductor of radius r1 and external conductor of radii r2 and r3. The material of the conductors has a conductivity \$\sigma_1\$. Between the conductors there is a imperfect dielectric of conductivity \$\sigma_2\$. I am asked to determine the conductance of the dielectric medium.
I have no problems doing the computation when I assume that the current density J has a radial direction. I come up with
My problem is understanding why the current is radial. I think I'm not correctly understanding the phenomena of stationary currents on dielectrics. I know that in this domain the electric field has 2 components: a normal one and a tangential one. The normal one is calculated the same way as it was in electrostatics, by applying Gauss Law. The tangential one, because of the continuity of the electric field is the same as inside the conductor. Now what I don't understand is how there is a current inside the dielectric. Is it because it's not a perfect one? But how is that current radial? Why that direction if the electric field has 2 components? Why don't we have a current in the same direction (longitudinal) as inside the conductors? Can anyone clarify me please? My questions are about the concept of electric currents on dielectric media, and not about the calculation of conductance.