Abstract: According to compact mathematical theory,we apply three kinds of methods to deduce the motional-induced expression from the flux expression of the electromagnetic inductive law.Thus it is claer that if on interval of [t,t＋dt） the loop does not break,the two expression forms will be equivalence at the moment of t.The mathematical theory about the rates of flux and circulation versus time is given.It is pointed out that the order of integral operation and differential operation should be exchanged.

Key words: electromagnetic inductive law, flux expression form, motional-induced expression form, equivalence