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Find the vector potentials

  1. Nov 8, 2007 #1
    1. The problem statement, all variables and given/known data
    A magnetic field of a long straight wire carrying a current I along the z-axis is given by the following expression:

    [tex] \mathbf{B} = \frac{\mu_0I}{2\pi} \{\frac{-y}{x^2+y^2} \hat{x} + \frac{y}{x^2 + y^2} \hat{y} \} [/tex]

    Find two different potentials that will yield this field. Show explicitly that the curl of the difference between these two potentials vanishes.

    2. Relevant equations
    [tex] \nabla \times \mathbf{A} = \mathbf{B} [/tex]

    3. The attempt at a solution
    I took a cross product to get this system...

    \frac{\partial A_y}{\partial x} - \frac{\partial A_x}{\partial y} = 0 \\

    \frac{\partial A_z}{\partial y} - \frac{\partial A_y}{\partial z} = \frac{-y}{x^2+y^2} \\

    \frac{\partial A_x}{\partial z} - \frac{\partial A_z}{\partial x} = \frac{y}{x^2+y^2} \\

    I dont know what to do! Any ideas?
    Last edited: Nov 8, 2007
  2. jcsd
  3. Nov 11, 2007 #2
    Maybe nobody knows how to do this problem...

    But does anybody know how to, in general, find a vector 'A' given its cross product 'B'?
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