Gauss' Law - difficulty understanding this example

[NewtonianAlch]

Homework Statement

[PLAIN]http://img851.imageshack.us/img851/5741/86853377.jpg

The Attempt at a Solution

For the long straight wire, the charge per unit length λ is already given, this is distributed on the surface of the wire. The electric field is zero for anything less than r1, because there is no enclosed charge inside the metal.

In the solutions booklet it says that the charge per unit length for the inner surface of the cylinder is -λ so that the internal charge adds to zero for r2 < r < r3.

What do they mean by that, and how did they get -λ ?

I understand that for r greater than r2, but less than r3, the same principle applies as it did earlier, the charge is on the surface, and no enclosed charge inside the metal, so therefore the electric field is zero inside. But why is -λ the charge per unit length for the inner surface of the cylinder?

 

[gneill]

The charge on the inner wire attracts an opposite charge to the inner surface of the cylinder. This charge is what neutralizes the electric field over the transition into the metal cylinder. Otherwise the electric field due to the charge on the inner wire would extend through the metal cylinder, and we know that this doesn't happen!

 

[NewtonianAlch]

Ah yes, that makes sense now that you put it that way! Of course...