Capacitance Calculation for Dielectric-Filled Coaxial Cable

[rude man]

Yes.

E is always radial, H is always along phi (in cylindrical coordinates) so P is always along z. I meant that the magnitudes change, not the direction.

 

[CAF123]

Yes.

E is always radial, H is always along phi (in cylindrical coordinates) so P is always along z. I meant that the magnitudes change, not the direction.

Many thanks for all your help. Last question: in the first part, if we were to do as you suggest and find D first (which I think makes more sense) rather than E, then how do you know that D is radial? Do we assume that the dielectric material has a linear susceptibility and hence that the D field inside the dielectric is related to the E field in a vacuum by the relation D = εE?

 

[rude man]

Many thanks for all your help. Last question: in the first part, if we were to do as you suggest and find D first (which I think makes more sense) rather than E, then how do you know that D is radial? Do we assume that the dielectric material has a linear susceptibility and hence that the D field inside the dielectric is related to the E field in a vacuum by the relation D = εE?

D is actually the sum of two vectors, one of which is ε₀E. The other is the so-called polarization vector P. P is associated with polarized charges only. In an isotropic medium, where a single ε_r can be assigned (i.e. regardless of direction), E and P point in the same direction. In an introductory course you are not likely to encounter non-isotropic dielectrics for which P can point in a different direction than E, and can depend on location and/or direction.