Abstract: By using the Maxwell＇s equations and axial symmetry, the axial symmetric unstable electromagnetic field with unstable charge source and unstable current source is studied. First, three elementary expressions are derived, then, the infinite series expression of electromagnetic field is obtained by using the known field expression in axial. At last, the convergence results is varified

Key words: axial symmetry, non-static field, Maxwell＇s equations, unstable source