Abstract: The function formula for the mutual inductance of the any two coaxial coils system is derived by the magnetic vector potential of a circular current. The images of the function varying to the distance of the two coils and to radius of the two coils equation of the magnetic induction is drawn scientifically and exactly by line from any two coaxial coils system mathematical software ＂MatLab＂. The is derived from the magnetic vector potential of a circular current yet. The distributional images of the magnetic induction line of coaxial coils system satisfying the equation is drawn by mathematical software ＂MatLab＂.

Key words: circular current, magnetic vector potential, elliptic integral, coaxial coils, mutual inductance, magnetic induction line, mathematical software ＂MatLab＂