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Cross product of magnetic fields

  1. Jan 14, 2010 #1
    Is there any physical meaning to the cross product of two magnetic fields e.g. two fields generated in two different current loops?
     
  2. jcsd
  3. Jan 14, 2010 #2

    Born2bwire

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    I do not think so, I am at a lost as to a situation where we would take the cross of two different magnetic fields. There is of course the usual geometrical interpretation of the cross product, indicating the anti-parallelism of the vectors, a normal to the vectors, etc., but that applies to any pair of vectors independent of their physical interpretations.
     
  4. Jan 14, 2010 #3
    Two loops will interact, if that's what you mean, so that the results are more than the sum of each.
     
  5. Jan 14, 2010 #4
    The reason I asked is that the cross product of the fields of two current loops tells you the work that one field would do on a magnetic monopole moving uniformly along the other loop.
     
  6. Jan 14, 2010 #5

    Born2bwire

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    But work is a scalar quantity, not a vector.
     
  7. Jan 14, 2010 #6
    True. The work is a scalar factor in the cross product. If you divide out by the work you get a fundamental generator of the second cohomology of R^3 minus the two loops. For instance if the work is zero the the cross product is the curl of another vector.
     
  8. Jan 15, 2010 #7
    What do you mean by "moving uniformly along the other loop." Are these loops supposed to be electric-current loops or magnetic monopole-current loops?
     
  9. Jan 16, 2010 #8
    Sorry - the monopole doesn't need to move uniformly. It just needs to make a complete circuit of the second loop. It's just that I am used to doing the integral using the unit of arc length.
     
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