# System of hollow cylindrical conductors

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1. Jul 10, 2015

### gruba

1. The problem statement, all variables and given/known data
Find potential and charge per unit length of every cylindrical hollow shell if the outer shell is grounded. The length is considered to be infinite.

2. Relevant equations
V=∫Edl

3. The attempt at a solution
I am not sure how to derive potentials for first two conductors (reference point is grounded third conductor). When integrating from (a to b)+(b to c) for the potential of the first conductor,
V1=1/(2πε0))*(ln(b/a)+ln(c/b))
V2=2/(2πε0))*ln(c/b)

Using superposition, charge per unit length of the third grounded conductor is
λ312

Now, what I don't understand is that the conductors are hollow. This system of shells can't be looked as cylindrical capacitor, right? Could someone check my equations and show how to do this if it is not correct?

Thanks for replies.

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2. Jul 13, 2015

### haruspex

If $\lambda_1$ and $\lambda_2$ are positive, what will the sign of the charge on the grounded conductor be?

3. Jul 13, 2015

### gruba

Ok, I solved the problem. Charge on the grounded charge will be negative.