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Integral problem on electric potential

  1. Oct 2, 2007 #1
    1. The problem statement, all variables and given/known data

    A long metal cylinder with radius a is held on the axis of a long, hollow, metal tube with radius b. The inner cylinder has positive charge per unit length [tex]\lambda[/tex], and the outer cylinder has an equal negative charge per unit length. Calculate the potential V(r) for r<a


    2. Relevant equations

    Va-Vb = [tex]\int[/tex]E.dr, where E can be found by Gauss's law

    3. The attempt at a solution

    My only problem is why the limit for the integral is from a to b even though r < a ??
    How does any point r < a experience a potential outside??
    [
     
  2. jcsd
  3. Oct 2, 2007 #2

    learningphysics

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    Homework Helper

    If you take the potential at infinity to be 0... then the potential at any radius r is,

    [tex]V(r) = -\int_{\infty}^r \vec{E}\cdot\vec{dr}[/tex]

    assuming b is the outer radius, and a is the inner radius

    [tex]V(a) = -\int_{\infty}^a \vec{E}\cdot\vec{dr} = -\int_{\infty}^b \vec{E}\cdot\vec{dr} - \int_{b}^a \vec{E}\cdot\vec{dr} [/tex]
     
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