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!

Potential of Infinite Wire

  1. Sep 29, 2013 #1
    1. The problem statement, all variables and given/known data
    [itex]\rho_{wire}=a[/itex], surface charge density [itex]\rho_S[/itex]

    What is potential difference of a point a distance of [itex]b[/itex] measured from the centre of the infinitely long wire, and the surface of the wire?

    Since all of the charge is dispersed on the surface of the conductor, there will exist no charge within the surface, and henceforth the electric field inside the conductor is zero. In addition, symmetry of the problem tells us that the electric field radiates outwards from the conductor.

    Let the origin be centred in the wire, such that the z-axis runs parallel to the infinitely long wire. We can apply Gauss's Law utilizing a gaussian surface such that [itex]\rho_{gaussian}=g > a[/itex], and the height from the xy-plane will be [itex]l[/itex].

    At this point, I just want to know if I am solving for the electric field properly. Thanks in advance.

    We know that
    [tex]\frac{1}{ε_o}\int _V \rho dV=\oint_S\vec{E}\cdot\vec{dS}[/tex]
    [tex]\frac{\rho_S(2\pi al)}{ε_o}=\oint_S\vec{E}\cdot\vec{dS}=E\int_SdS=E(2\pi gl)\rightarrow E = \frac{\rho_Sa}{b}[/tex],
     
    Last edited: Sep 29, 2013
  2. jcsd
  3. Sep 30, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    The only mistake you made was to omit ε0 in the denominator.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Potential of Infinite Wire
  1. Infinite Series (Replies: 1)

  2. Wire ORed (Replies: 3)

  3. Wire gauge (Replies: 7)

  4. PIC Wiring (Replies: 3)

Loading...