Current loop + perpendicular current : magnetic field?

[el_greco]

Homework Statement

Hi, it's my first post and I'm not sure whether it's the right category to post anyway. Please help me though :) I have to "construct" theoretically a superposition of magnetic fields for the introduction of my tokamak-related diploma thesis. First task was to find the magnetic field due to a current loop, which was done with elliptic integrals and the ellipke function in matlab. Then I had to superimpose a perpendicular current at the centre of the loop and plot the total magnetic field. That was easy, since I just had to add a new quantity to the already existing Br part of the current loop imposed field.

My problem now is what happens when the perp. current is not perp. any more, but crosses the plane of the loop at an angle theta. What's more, it's not even in the centre anymore, but at some other part of the diameter, along the r axis of the cylindrical system.

What is the specific change at the coordinates' system I have to apply so as to express the new magnetic field in the old coordinates, Br and Bz of the current loop (which is still there) ? Eventually I'll have to add this to my plot...

I'd appreciate any help, and please tell me whether you would like to see the m-files etc...

Thank u!

 

[Gokul43201]

You need to tranform between cylindrical co-ordinates that are tilted relative to each other. Since the rotation is about a single rectangular axis, you can simply use the 2-d rotation matrix to achieve this. But this is only good for rectangular co-ordinates, so you'd have to convert from cylindrical to rectangular, then rotate the axes, then convert back to cylindrical and add to the field from the circular loop.

There's probably a cleverer way to do this, but the above should work.