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I Magnetic vector potential of infinite straight wire

  1. Aug 30, 2016 #1
    The magnetic field generated by an infinitely long straight wire represented by the straight line ##\gamma## having direction ##\mathbf{k}## and passing through the point ##\boldsymbol{x}_0##, carrying a current having intensity ##I##, if am not wrong is, for any point ##\boldsymbol{x}\notin \gamma## $$\boldsymbol{B}(\boldsymbol{x})=\frac{\mu_0 I}{2\pi}\frac{ \mathbf{k}\times (\boldsymbol{x}-\boldsymbol{x}_0) }{\| \mathbf{k}\times (\boldsymbol{x}-\boldsymbol{x}_0) \|^2}.$$
    I wondered whether the vector potential ##\boldsymbol{A}## such that ##\nabla\times \boldsymbol{A}=\boldsymbol{B}## exists and what function it is...
    I ##\infty##-ly thank you for any answer!
     
  2. jcsd
  3. Sep 2, 2016 #2

    DrDu

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    Science Advisor

    Try to convert your problem to cylindrical coordinates.
     
  4. Sep 2, 2016 #3
    After some trials and a bit of intuition I have found a vector field whose curl is ##\boldsymbol{B}##:$$-\frac{\mu_0 I}{2\pi}\ln\|\mathbf{k}\times(\boldsymbol{x}-\boldsymbol{x}_0)\|\mathbf{k}$$
     
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