Finding the Electric Field in a Coaxial Cable with Volumetric Charge Density

[satchmo05]

Homework Statement

Consider a coaxial cable that consists of inner/outer conductors of radii a and b, and it is filled with electron cloud with volumetric charge density of ρ_v = Υ/ρ [C/m³] for a < ρ < b. If outer conductor is +V_o [V] more positive than inner conductor, find E field between conductors.

Homework Equations

ρ_v = Υ/ρ = ∇*D = ∇*єE = ∇*(є_oE + P)

Also, E for coaxial cables in this scenario is (+E_o/ρ)a_ρ, where ρ = 2(b-a)

The Attempt at a Solution

The farthest I can get is what I have for the equations above. Can anyone give me any helpful hints to get me going in the right direction. Thank you much for all help!

 

[anathema]

Hi! It seems like you have the right equations to start with. To find the electric field between the conductors, you can use Gauss's Law, which states that the electric field at a point is equal to the charge enclosed by a closed surface divided by the permittivity of free space. In this case, the charge enclosed would be the charge density multiplied by the volume between the conductors (π(b^2-a^2)). So you can set up the equation ∮E•dA = Qenc/єo and solve for E. Does that help?