In the teaching of electromagnetics in college physics, it is a very classical problem to solve the magnetic field excited by a current carrying circular coil. When dealing with this kind of problem, the traditional method is to use Biot Savart's law for vector integration The integral formula obtained by this method can not be expressed by elementary functions, and can only be approximated to the dipole form in the far field case In this paper, an innovative solution is proposed, in which the magnetic scalar potential is introduced into the space without free current to solve the Laplace equation; By using the field strength on the axis to determine the solution, the tedious process of matching the boundary conditions is avoided, and the series solution of the magnetic induction is successfully obtained Through numerical calculation, it is verified that the solution obtained by this method is consistent with the result obtained by the vector integral method, which is of great significance in electromagnetics teaching.