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Magnetic vector potential for antiparallel currents

  1. Oct 28, 2012 #1
    Two infinitely long wires separated by distance d. Currents: I1 = -I2. Find potential vector as a function of r1 and r2 at a point P (r1 and r2 distances to P from wire one and wire two).
    Del cross A= B
    B = (mu I)/(2pi r)



    Using Ampere's, I get an expression for the magnetic field that involves two different distances, r1and r2. I see that integrating this expression with respect to distance will give me the vector potential. But with two distances to take into account, I don't know how to solve this.
     
  2. jcsd
  3. Oct 28, 2012 #2
    Oh I'm using cylindrical coordinates. With the wires oriented along the z axis, the only term that survives del cross A is the azimuthal component.
    -partial dA/ds = (mu I)/2pi [(1/r1) - (1/r2)] in the phi direction.
     
  4. Oct 28, 2012 #3

    TSny

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    Gold Member

    Hello.

    Can you find an expression for A for a single infinitely long straight wire carrying current I ? If so, then the superposition principle will get you the answer fairly easily.
     
  5. Oct 29, 2012 #4
    Thanks TSny. Duh... the problem asks me to get the vector as a function of two different distances. I don't need to find a way to relate them. QuiteEasilyDone
     
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