Magnetic field generated by a circular current loop

[ramses728]

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.

 

[marcusl]

This is presented in all standard E&M books. Take a look at
Jackson, Classical Electrodynamics or
Smythe, Static and Dynamic Electricity

 

[ramses728]

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?

 

[marcusl]

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

http://www.netdenizen.com/emagnet/offaxis/iloopoffaxis.htm"

 

[lstookey]

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.

 

[ramses728]

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

 

[el_greco]

I believe what you are looking for is extensively analyzed here:

http://plasmalab.pbwiki.com/f/bfield.pdf

 

[Troels]

Oh my... I've been searching for that field for years! Thank You!

 

[pam]

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.

 

[gattu]

I believe what you are looking for is extensively analyzed here:

http://plasmalab.pbwiki.com/f/bfield.pdf

the link is useful. thanks for this pdf link...

 

[gattu]

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...

 

[pieselsoft]

For a new derivation, see:
http://dx.doi.org/10.1088/0143-0807/27/5/N01

 

[Meir Achuz]

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.