Abstract: The series expansion method is used to get the exact infinite series expression of the mutual inductance between two coaxial circular coils in general situation.The infinite series is convergent in all cases except for the two coils coincide with each other.Moreover,vector potential,instead of magnetic induction,is used to calculate the magnetic flux,which makes the method more convenient.

Key words: mutual inductance, coaxial coil, circular current loop, magnetic vector potential, infinite series