Today I tried to solve the value the magnetic field vector at an arbitrary position for a field generated with simple coils such as a circle or a square. For the circle coil, the analytical expression of the field can not be expressed using common functions (exp, log, tan…). I still hope to express the “unexpressible” primitive functions with easy-to-compute series. For the square, the field can be calculated quite easily but the answer is long and ugly. Moreover, if we buy coils for the project, they will probably be circular.

I also searched for documents the matricial Newton-Raphson method. We will probably use to solve for the position of the of the receiver using the formula of the magnetic field vector.

Next, I need to continue the calculation of the magnetic field for a circular coil.

It’s been a long time I studied electromagnetism, but I seem to remember something about the field generated by a cylindrical coil having something to do with Bessel functions (http://en.wikipedia.org/wiki/Bessel_function). Might be worth digging.

Thanks for your help 🙂 I made some research and it seems the functions I need are first-kind and second-kinds elliptic integrals. I think bessel functions are mostly used in elctromagntics to express diffraction by a circular aperture.