Abstract: The Ampere circuital theorem is an important law in stationary magnetic fields and is

often used to analyze the magnetic flux intensity of a current system with a certain symmetry. The

useful conditions of the Ampere circuital theorem and its mathematical principles are studied. The

misunderstanding that the Ampere circuital theo- rem is incorrect in a finite-length

current-carrying straight wire system is clarified through a simple model. The uni- versality of

the Ampere circuital theorem is exemplified. It helps students to master Ampere circuital

theorem and understand the properties of magnetic fields.

Key words: Ampere circuital theorem, useful conditions, magnetic flux density