1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


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


    ..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


    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


    User Avatar


    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

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook