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Potential of two parallel infinite wires

  1. Feb 13, 2014 #1
    1. The problem statement, all variables and given/known data
    Two parallel infinite wires lay parallel to the z-axis in the xz-plane. One located at x=d has charge distribution λ and one located at x=-d has charge distribution -λ.


    2. Relevant equations

    a) Find the potential V(x,y,z) using the origin as a reference
    b)Show that the equipotential surfaces are circular cylinders parallel to, but not coaxial with, the wires. For a given V_0 determine the corresponding axis and radius of the cylinder.

    3. The attempt at a solution

    I believe we can approach this problem with gaussian surfaces, but i am confused on how to exactly use the fact that the origin is a reference. Also the fact that its in cartesian is messing with my ability to do the problem, there is so much cylindrical symmetry...
     
  2. jcsd
  3. Feb 13, 2014 #2

    Simon Bridge

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    Normally you'd do this problem for one wire, with the wire along the x axis or similar.

    This gives you an equation for the electric field about that axis.
    What happens to that equation if the wire is not on the axis?

    Hint: if a simple parabola were centered on the y axis it would have equation ##y=x^2##, if it were now centered on the line x=d, it would have equation ##y=(x-d)^2##.
     
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