How to Determine Charge Distribution in a 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 \lambda

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

Homework Equations

\lambda= Q / L

\phi= EA = 2\pirL = Q / \epsilon_{0}

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 \lambda / 2\pir\epsilon_{0}.

But I have no idea how to find \lambda_{inner} or \lambda_{outer}

 

[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 \lambda / 2\pir\epsilon_{0}.

But I have no idea how to find \lambda_{inner} or \lambda_{outer}

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?