Formulas for the magnetic field of polygonal cross section current coils

An extension to the case of general polygonal cross section of the analytical expressions obtained previously by the author for the magnetic field of rectangular-cross-section current coils is presented. The polygonal-cross-section coils are decomposed in straight segments whose sides along the current direction are trapezoidal in general. By using surface source models, the field due to the volume current distribution is expressed in terms of that due to sources distributed over the segment side surfaces, for which simple formulas are derived. All these formulas contain elementary functions only, and numerical results, even for the special case of rectangular-cross-section coils, show a substantially higher computational efficiency than can be obtained with previous methods.>