Magnetic field generated by a circular current loop

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Discussion Overview

The discussion revolves around determining the magnetic field generated by a circular loop of current, with specific interest in its application to the poloidal field in a Tokamak. Participants explore various methods and resources for deriving the magnetic field, including the Biot-Savart Law and alternative mathematical approaches.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant, ramses, expresses difficulty in determining the magnetic field using the Biot-Savart Law and seeks a complete vector field description.
  • Another participant suggests consulting standard E&M textbooks, specifically mentioning Jackson and Smythe.
  • Some participants mention challenges in accessing these texts, particularly those located far from academic libraries.
  • Links to online resources are shared, including a derivation from netdenizen.com and a PDF from plasmalab.pbwiki.com, which some find helpful.
  • There is mention of simpler treatments using Legendre polynomials in Franklin's "Classical Electromagnetism," which some participants believe could aid in understanding off-axis magnetic fields.
  • One participant argues that analytical solutions without advanced mathematical tools like Legendre polynomials or Green's functions may not be feasible, suggesting numerical methods instead.
  • New derivations are referenced, including a link to a publication that presents a more complex approach involving spherical harmonics.

Areas of Agreement / Disagreement

Participants express a range of opinions on the best methods to derive the magnetic field, with no consensus on a single approach. Some advocate for analytical methods while others suggest numerical solutions, indicating ongoing debate and exploration of the topic.

Contextual Notes

Participants note limitations in their current resources and the complexity of the mathematical approaches required, highlighting the dependence on advanced mathematical techniques for analytical solutions.

ramses728
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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.
 
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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
 
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?
 
Oh, how fun! Well, the result is quoted here without derivation

http://www.netdenizen.com/emagnet/offaxis/iloopoffaxis.htm"
 
Last edited by a moderator:
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.
 
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
 
Oh my... I've been searching for that field for years! Thank You!
 
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.
 
  • #10
  • #11
without Legendre polynomials or Greens functions or elliptical functions usage ,,,u can't solve this problem analytically,,,,,,,better try numerical methods for a simple treatment...
 
  • #13
pieselsoft said:
For a new derivation, see:
http://dx.doi.org/10.1088/0143-0807/27/5/N01
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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