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Electric potential due to long wire

  1. Jun 1, 2007 #1
    1. The problem statement, all variables and given/known data
    Using Gauss' law, or otherwise, find an expression for electric potential at a distance r from an infinitely long straight line of charge of length h with linear charge density lambda per unit length.

    2. Relevant equations

    q=lambda*h


    3. The attempt at a solution
    The first part is easy, using gauss' law to find electric field..the result i get is

    E=lambda/(2*pi*r*epsilon_0)

    ..which should be correct. But then i'm not sure how to find potential in this case. I tried using the equation:

    E= - grad*V

    so

    V = integral[E*dl]

    V= -lambda/(2*pi*epsilon_0) integral_from_infinity_to_r[(1/r) dr]

    ..which leads me to:

    V = -lambda/(2*pi*epsilon_0) [ln(r)]

    where the ln(r) is evaluated from infinity to r...and im not sure that looks right, or where to go from there.. :confused: I don't know what the solution is supposed to be and I couldn't find any explanations when i googled it..anyone have any idea??? :uhh: thankyou sooo much!!!!
     
  2. jcsd
  3. Jun 1, 2007 #2

    Dox

    User Avatar

    Hello.

    In fact that's the solution. That's life!
     
  4. Jun 2, 2007 #3
    heh :redface: thankyou!!
     
  5. Jan 25, 2010 #4
    how do you evaluate ln at infinity and r??
     
  6. Feb 10, 2010 #5
    pick an arbitrary point a, and integrate with respect to that point. you're correct that you can't integrate to an infinite potential at the wire.
     
  7. Apr 19, 2010 #6
    the only way i can think of is that u have to assume the boundary condition that V=0 at infinity. but then that seems forced because when evaluating the similar case for a sphere u get a 1/r term and when u plug in infinity there it goes to zero (see griffiths 3rd ed example 2.6). can anyone reconcile these cases? i don't see any explanation above addressing this.
     
  8. Sep 22, 2010 #7
    Hi,

    You cannot use infinity, because the problem states that there is an infinite length of wire. This tells us that the charge is infinite. Using a variable like "a" is your best bet for solving the problem.
     
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