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Magnetic field generated by a circular current loop

  1. Nov 26, 2007 #1
    Hello everybody!
    I have some trouble determinating the magnetic field generated by a circular loop of current. I'd use it as an approximation for the poloidal field in a Tokamak (field generated by the current in the plasma).
    I tried using Biot-Savard's Law but I'm getting stuck... I hope to get an answer soon

    greets ramses

    P.S. I'm not looking for the field in the middle of the current loop, I need the whole description vector field.
  2. jcsd
  3. Nov 26, 2007 #2


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    This is presented in all standard E&M books. Take a look at
    Jackson, Classical Electrodynamics or
    Smythe, Static and Dynamic Electricity
  4. Nov 26, 2007 #3
    Thanx, but I think I'll have some difficulties getting those books... I'm in the italian speaking part of switzerland, but I'll give a try to my school library.
    If there is some kind of electronic version on this specific topic, could someone link it plaese?
  5. Nov 26, 2007 #4


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    Last edited by a moderator: Apr 23, 2017
  6. Nov 26, 2007 #5
    I've been looking for the same thing - off-axis magnetic field strength at a distance from the source of the field. All my university physics texts give the on-axis derivation (or at least binomial approximation), but hold short of off-axis derivations for B. I contacted Eric Dennison at netdenizen.com (see previous post by Marcus!). He thinks he has a derivation. I am hoping to hear from him shortly. I'm probably as bad off as ramses728, up in the north woods of Wisconsin, USA. The nearest source for these texts is about 250-300 km away.
  7. Nov 27, 2007 #6
    I understand your situation Istookey, no one here where I live has some real good clue how to solve this problem. I tried some ways through the biot savard law but had not much luck... And just having those formulas written does not help me really much how to get there... I'll try again now see if i get something out of it.

    If you Eric Dennison from netdenizen.com replies let me know.

    greets ramses
  8. Dec 29, 2007 #7
  9. Jan 3, 2008 #8
    Oh my... I've been searching for that field for years! Thank You!
  10. Jan 4, 2008 #9


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    There is a simpler treatment using Legendre polynomials in the book "Classical Electromagnetism" by Franklin. It also treats the off-axis magnetic field of a solenoid or bar magnet.
  11. Nov 18, 2008 #10
  12. Nov 18, 2008 #11
    without Legendre polynomials or Greens functions or elliptical functions usage ,,,u cant solve this problem analytically,,,,,,,better try numerical methods for a simple treatment.....
  13. Dec 9, 2008 #12
    Last edited by a moderator: Apr 24, 2017
  14. Dec 9, 2008 #13


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    That is an interesting derivation, but it is more complicated than using the magnetic scalar potential. The delta function derivation is particularly tricky as he does it.
    That could have been proven more easily using spherical harmonics.
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