Solve Image Charge Problem: No Quotes

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The discussion revolves around understanding the potential of a charged cylinder relative to a plane, with confusion about the application of Gauss's theorem and the symmetry involved. The potential is suggested to be -q/2πε ln r, but the implications of charge distribution induced in the plane are also highlighted. Participants note that calculating the work needed to move the cylinder to infinity could yield the desired answer. The method of images is identified as the correct approach, though there are concerns about inconsistencies in the calculations presented. Overall, clarity on these concepts is essential for solving the image charge problem effectively.
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Homework Statement


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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]
KakaoTalk_20170320_215526648.jpg
 
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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 ?
 
BREAD said:
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.
 

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