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Does this answer look right? (Infinitely long conductor pipe)

  1. May 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Fig. 1 shows the cross-section of an infinitely long conducting pipe. The inner radius of the pipe is r = R1, and the outer radius is r = R2. Suppose the inner surface has a constant voltage V = Vc > 0, and the outer surface has a constant voltage V = 0. The voltage distribution between the inner and outer surface (blue region) is governed by the Laplace's equation ∇2V=0 expressed in polar coordinates. Solve for V with the given boundary conditions.

    [Note: Fig. 1 just looks like a blue annulus centered at the origin in the plane.]

    2. Relevant equations

    Don't worry about them for now.

    3. The attempt at a solution

    Just tell me whether my solution V = (Vc log(r) - log(R2))/(log(R1) - log(R2)) intuitively seems like it's correct. I don't want you to carry out the process of deriving this ..... unless you want to.
  2. jcsd
  3. May 7, 2012 #2
    I.e. the voltage at a distance r from the center of the piper is proportional to log(r)
  4. May 8, 2012 #3

    Actually I got

    V(r,θ) = Vc * [log(r) - log(R2)] / [log(R1) - log(R2)]. ​

    Does that seem right?
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