Magnetic field, vector potential, and their partial derivatives due to a current-carrying straight wire of finites length

A numerical study is made of a problem dealing with calculation of the magnetic field B vector, the magnetic vector potential A vector, and first partial derivatives of the B vector field and A vector components for two kinds of magnetic sources: (1) current-carrying straight wire of finite length; and (2) current-carrying closed polygon. No restrictions are imposed on the type of the polygon and hence it need not be plane and can consist of an arbitrary number of straight wires of arbitrary lengths. Separate consideration of the polygon case makes the numerical procedures more efficient than that based on the linear superposition of the straight-wire sources. All necessary quantities are derived analytically in simple and closed forms without use of any approximations and exact relations are utilized to the greatest possible extent to give an efficient algorithm. Thus, the involved numerical procedures are quite simple, fast, accurate, and straightforward. Results are given in four different coordinate systems (cartesian, cylindrical, spherical, and local toroidal).