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Electric potential

  1. Apr 25, 2007 #1
    1. The problem statement, all variables and given/known data

    There is an infinite conducting charged metallic wire. What will the potential at a distance r from the wire be?



    3. The attempt at a solution

    I know that [tex]E=\frac{\lambda}{2\pi \epsilon r}[/tex] and [tex] E=\frac{-dv}{dr}[/tex].

    Integrating the expression for the electric field wrt r, [tex]V(r)=-\frac{\lambda}{2\pi \epsilon} logr[/tex]

    This, however, isnt the answer. Why?
     
  2. jcsd
  3. Apr 25, 2007 #2

    Mentz114

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    You should be integrating the field from an element of the wire from -inf to +inf.
     
  4. Apr 25, 2007 #3
    Ouch. That would make it undefined at that point, right?
     
  5. Apr 25, 2007 #4

    Mentz114

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    Assume you have linear charge density r, so the charge of a line element is r.dl. The electric field at point r is k.r.dl/(r^2+l^2).
     
  6. Apr 25, 2007 #5
    I can figure out the expression for the electric field, but its the potential I had the question about. Wont it be undefined?
     
  7. Apr 25, 2007 #6

    Mentz114

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    Rats, I misread the question. Integrating the potential of a line element blows up because it's a scalar. It really does look as if there's nothing you can differentiate to give the 1/r dependence.
     
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