# Methods of Images between two parallel cylinder

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1. Jan 24, 2016

### flux!

1. The problem statement, all variables and given/known data
Using methods of Images, How do I find the potential of the system consisting of two conducting cylinders that are not grounded and separated at a distance of 2D, one in a potential of $V_0$ and the other is $-V_0$?

2. Relevant equations

The potential due to an infinite line charge is given by
$$V = \frac{\lambda}{2\pi \varepsilon}ln|\frac{b_{ref}}{r}|$$

3. The attempt at a solution

This does not necessarily require solution since the final potential is just the sum of the equation above. But I could get wrong In analyzing how many potentials are involved.

So by methods of Images,

1. We got to first determine the line charge that produce the present potential on each cylinder, which was fairly as simple as using the equation above, then changing pertinent variables. So that already 2 potentials.

2. Next, we got to account for the potential induced by each conducting cylinder to each other, so that is its image. So that is another two potential.

3. Over all we will have 4 potentials affecting any point outside each cylinder, but well, when I looked at the final answer, its just two potential. Moreover, my own answer does not jive with the correct solution of the same problem I have solved without using Methods of Images. Clearly, something went unusual to my analysis of the problem.

4. In summary

What should be the right way of doing methods of Images for this problem?

Last edited: Jan 24, 2016
2. Jan 29, 2016