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Current distribution diagram confusion!

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data

    I am trying to interpret a diagram of a current distribution, with a view to finding the vector potential. I 'm afraid I don't know how to put images here, so I will try to describe it.

    In the diagram the x-y plane faces the viewer.
    In the x direction the diagram shows two arrows facing towards each other.
    In the y direction the diagram shows two arrows facing exactly away from each other.
    Next to each arrow there is a lower case i.



    3. The attempt at a solution

    I think it means that the magnitudes of the currents are equal but in different directions. They converge on x and diverge on y, but I'm not sure if this is right, or possible? It seems unlikely to me.
    If this is correct and I'm not missing anything my solution to finding the vector potential would be simply to make a sum of its x,y,z components. It looks like they would cancel to me though.

    If anyone could tell me if i'm on the right track or nudge me in the right direction I would be very grateful!
     
  2. jcsd
  3. Feb 23, 2009 #2

    LowlyPion

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    If you are saying they converge at the origin from -x,x and flow away -y,y, then so long as you observe Kirchhoff's Current Laws, the conservation of charge, then it's possible.
     
  4. Feb 23, 2009 #3
    That was fast thanks! Yep, thats what I was trying to say. I am only dealing in magnetostatics at the moment so I think charge must be conserved, otherwise the magnetic field would vary, is that right?

    Also, could you give me an example of this situation? I'm having trouble visualising it..
    Thanks for your help!
     
  5. Feb 23, 2009 #4

    LowlyPion

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    Without wires, you know those convenient conductors, I am presuming that you would be talking about a stream of electrons flowing in space. If say two streams encountered a uniform magnetic field region, heading toward each other, one would imagine that the Lorentz force relationship would introduce a directional translation. One to the left and one to the right. Let the right hand rule be your guide.

    (Remember at all times you were asking about possible.)
     
  6. Feb 23, 2009 #5
    I see what you mean.

    Thanks

    Last thing, to your knowledge does little Xi ever have a particular meaning in magnetostatics or does it just refer to some small increment?
     
  7. Feb 23, 2009 #6

    LowlyPion

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  8. Feb 23, 2009 #7
    No, I just meant the greek letter. I think it does just mean a small increment but I missed todays lecture and I'm not quite sure, trying to catch up now.
    Thanks for all your help
     
  9. Feb 23, 2009 #8

    LowlyPion

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    Well catch up then, and good luck.
     
  10. Feb 23, 2009 #9
    cheers!
     
  11. Feb 24, 2009 #10
    Hi again,

    Now I was wondering if someone could tell me if this is reasonable, for the x component of the vector potential A(r) I have found that

    Ax = -u*I*xhat/(4*Pi) ln((y+sqrt(x^2+y^2+z^2)/(-x+sqrt((-x)^2+y^2+z^2)))

    I'm not exactly convinced.

    I find similar for y but for z i think it is simply zero, but I'm not sure if it is ok to just state this.
    I was working in cartesian coordinates, but it occurs to me that maybe i ahould use curvilinear because of the shape of A, but then I wouldn't know what to do at the intersection of the currents.

    Also any latex advice, other peoples equations look much better...

    Thanks

    #edit- just adjusted the brackets
     
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