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a few days ago I derived the probably well-know expression for the magnetic field of a current loop including elliptic integrals of the first and second kind (it can be seen here http://plasmalab.pbworks.com/f/bfield.pdf ). As I'd like to rotate and shift the position of the current loop I tried to transform the expressions for the fields [tex] B_r, B_z [/tex] into cartesian coordinates but failed because i also need to transform the elliptic integrals and I don't know how to do that.

Do you think I have to derive the whole thing again (starting with the current density's in x-,y- and z-direction but now strictly in cartesian coordinates which is very tedious) or is there a way to get the wanted cartesian expression from the one's in cylindrcal coordinates which I have already written down.

Thanks for your comments !

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# Off-axis magnetic field due to a current loop in cartesian coordinates

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