Gaussian Surface, Coaxial Cable

[mvpshaq32]

Homework Statement

A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length [tex]\lambda[/tex]

Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.

Homework Equations

[tex]\lambda[/tex]= Q / L

[tex]\phi[/tex]= EA = 2[tex]\pi[/tex]rL = Q / [tex]\epsilon_{0}[/tex]

The Attempt at a Solution

I solved in previous parts that the magnitude of the electric field at any point between the cylinders a distance r from the axis and the magnitude of the electric field at any point outside the outer cylinder a distance r from the axis is both [tex]\lambda[/tex] / 2[tex]\pi[/tex]r[tex]\epsilon_{0}[/tex].

But I have no idea how to find [tex]\lambda_{inner}[/tex] or [tex]\lambda_{outer}[/tex]

 

[tiny-tim]

hi mvpshaq32!

(have a phi: φ and a pi: π and an epsilon: ε and a lambda: λ )

I solved in previous parts that the magnitude of the electric field at any point between the cylinders a distance r from the axis and the magnitude of the electric field at any point outside the outer cylinder a distance r from the axis is both [tex]\lambda[/tex] / 2[tex]\pi[/tex]r[tex]\epsilon_{0}[/tex].

But I have no idea how to find [tex]\lambda_{inner}[/tex] or [tex]\lambda_{outer}[/tex]

call the (constant) electric field inside the outer cylider E1, and the charge-per-length on its surfaces ±µ …

then what are the two equations for the change in field as you cross each of the two surfaces?