Simple analytical expressions for the magnetic field of current coils

Current coils are decomposed in straight segments of rectangular cross section whose sides are trapezoidal in general. For curved coil portions, the appropriate number of straight segments is considered in terms of the desired accuracy. Simple formulas are derived for the contribution of such a coil segment to the resultant magnetic field by modeling the given volume current density in terms of a distribution of fictitious magnetization inside the segment volume and corresponding surface currents and magnetic charges. The expressions obtained contain only elementary functions, and computed results illustrate their efficiency with respect to existing analytical and numerical integration methods