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E/M Vector Potential of finite Wire

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider a finite wire which lies on the z-axis and extends from the point z=-Λ to the point z=+Λ. The vector potential in the xy plane a distance s from the wire is:
    A=(µₒI/2π) ln (2Λ/s) k̂

    An equally good vector potential is given by A'=A+∆λ, where λ is any scalar field we wish to choose. Determine a suitable choice for λ which has the property that A' remains finite in the limit Λ->∞.
    (Let ∆ be rotated 180 to be the gradient.)

    2. Relevant equations

    I found the curl of A=(µₒI/2π) ln (2Λ/s) k̂ to find the magnetic field, and I got:
    A*= -(µₒI/2πs)

    3. The attempt at a solution
    Ok, here is what I did:
    I figured that I had to find a value of λ that gave way to a A' that when you took the curl of it would yield A*. At first, I just tried to find a value of λ that was involving ln (...)k̂,
    but then I saw that A' would then depend (s), and it would be tricky to find a value. Then I saw the hint that it was better if λ didn't depend on (s).

    So, if I just want A, can I just choose a random constant for λ? Like 4 or something?

    Please Help!!
  2. jcsd
  3. Dec 9, 2008 #2


    User Avatar
    Gold Member

    For the derivative in the curl of A, remember the chain rule (derivative of the outside times the derivative of the inside).

    As for the star question, since z goes to infinite perhaps you could view this in terms of an angle instead of a distance.
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