Solve Image Charge Problem: No Quotes

[BREAD]

Homework Statement

Homework Equations

The Attempt at a Solution

I don't understand what is the meaning of "potential of cylinder relative to the plane"
I think the potential of cylinder is just -q/2πε ln r by Gauss's theorem[/B]

 

[BvU]

What symmetry is there that you use in the Gauss theorem ? Does that apply here ?
What does the $\Phi$ you write down represent ?

It will require a certain amount of work to drag the cylinder to infinity. Isn't that work, divided by the charge, the answer the exercise ants from you ?

 

[haruspex]

the potential of cylinder is just -q/2πε ln r by Gauss's theorem

The cylinder will induce a charge distribution in the plane. That in turn will affect the potential at the cylinder.
You attach some working but don't explain it. The method of images is certainly the right way, but it looks like a z+d got changed to a z-d at the second line.