Aim To quantitatively analyze and explain the A-B effect, and potential A has the physical effect which may been observed. Methods Feynman's path integral and quantum theory are used to analyze quantitatively phase shift of electron probability wave resulting from the magnetic vector-potential A and then the A-B effect is explained. Results Although the electronic movement goes to region without any action to exert on the electronic, some extra factor attaches actually in the electronic probability wave,and appears the interference fringe move...