Question on the nature of induction

[hamhamt]

Homework Statement

A long, straight wire is surrounded by a hollow metallic cylinder whose axis coincides with that of the wire. The solid wire has a charge per unit length of + λ, and the hollow cylinder has a net charge per unit length of +2λ. From this information, use Gauss's law to find:

(a) the charge per unit length on the inner and outer surfaces of the hollow cylinder

(b) the electric field outside the hollow cylinder, a distance r from the axis

Homework Equations

λ = \stackrel{Q}{A}

The Attempt at a Solution

i'm not sure if my reasoning is correct, but this so far this is what i think based off a similar problem from the book:

since the line charge is +L, by induction, the inner surface of the cylinder is -L. consequentially, is the outer surface is the +L because of the polarization of the charge on the cylinder by the line charge?

i am not sure about how the line charge affects the outer surface of the cylinder, can anyone elaborate on this?
also, how does the polarization by the line charge affect the total charge of the system, at a distance larger than the radius of the cylinder? would this then be +L + +2L = +3L?

 

[Simon Bridge]

Just apply Gausses law.

 

[hamhamt]

i know i am supposed to apply gauss's law. the question tells you to use gauss's law.

i am unsure about what Q Enclosed is at certain regions, and is what I describe I was having issue with at the end of my post.

 

[Simon Bridge]

You are trying to do too much in advance of the calculation.

I'd try using the differential form of Gauss' law for this myself.
Pick an appropriate symmetry, and divide the volume into appropriate regions.
Solve the DE for each region - then apply the boundary conditions.
You'll have a bunch of equations which can be manipulated to help answer your questions.What does the electric field between the walls of the cylinder have to be?
If there were no line charge in the center - what distribution of charge would achieve this and why?