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$$\pi$$rL = 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$$\pi$$r$$\epsilon_{0}$$.

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$$\pi$$r$$\epsilon_{0}$$.

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?