Changes

The magnetic field emitted by each coil is modelled using the current filament method described by [https://pure.tue.nl/ws/files/2417049/Metis213041.pdf Sonntag et al.]. Each straight-line copper 'filament' of the PCB coil is treated as a uniform individual current-carrying conductor. The magnetic field due to each filament is calculated using the Biot-Savart law. The field strength from each individual are added using superposition to provide the total magnetic field of the PCB coil. The diagram below shows a single current-carrying filament with current II <math>I</math> being observed from a point <math>P=(x,y,z)P</math>.  The magnetic field strength at PP due to the filament is given by:<math display="block">{B(r)} = \frac{\mu_0 I}{4 \pi} \sum^n_{i=1} \left(x\frac{c_i \times a_i}{|c_i \times a_i|^2}\right) \left(\frac{a_i . c_i}{|c_i|} - \frac{a_i . b_i}{|b_i|}\right)</math> where <math>a_i</math> is a vector in the direction of the filament, <math>b_i</math> is a vector pointing from an observation point <math>p</math> to the end of the filament, and <math>i_c</math> is a vector pointing from <math>p</math> to the start of the filament. <math>n</math> represents the total number of filaments in the coil, while ii is the filament under consideration. The equation above requires the coordinates of each PCB filament to be precisely known. The square nature of the emitter coils makes this calculation simple to perform. The PCB fabrication parameters (trace length,yspacing,ztrace thickness) are shown in the table below. These parameters are used to iteratively calculate the coordinates of each current filament for N turns of a PCB coil.[[File:Coilparams.PNG|center|400px|caption]]Code for determining the Anser EMT coil filaments is available in the repository. (The first image on this page was generated in Matlab using this code).