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Retarded Potentials

  1. Feb 15, 2007 #1
    1. The problem statement, all variables and given/known data
    Suppose a wire carries a current such taht
    I(t) = 0 for t< = 0
    = k t for t > 0
    Find the electric and magnetic fields generated

    2. The attempt at a solution
    trying to figure out vector potential first
    looking at the diagram
    s is the distance fro a point P to the wire which is positioned on the Z axis.
    r' is the distance to some section of the wire dz

    the only contribution is for t > s/c, otherwise the em fields havent reached the point P

    we only need to integrate along the z since there is X and Y symmetry

    [tex] z = \pm \sqrt{c^2 t^2 - s^2} [/tex]
    but we are going to get the EM fields from time [itex] = t - r' / c = t - \frac{\sqrt{z^2 + s^2}}{c} [/itex]

    so we're lookign at integrating this

    [tex] A = \frac{\mu_{0}}{4 \pi} 2 \int_{0}^{\sqrt{c^2 t^2 - s^2}} \frac{k (t-\frac{\sqrt{z^2 + s^2}}{c}}{\sqrt{z^2 + s^2}} dz [/tex]

    ahve i gone wrong somewhere??

    something wrong in my logic?

    please help!

    thanks for any and all input!

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  2. jcsd
  3. Feb 18, 2007 #2
  4. Feb 18, 2007 #3


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    Gold Member

    That looks correct to me
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