Fundamental equations for eddy current analysis by using the A-φ method and 3-D analysis of a conducting liquid

The fundamental equation for the A-φ method is formulated using Maxwell´s equations and the continuity equation for electric charge. Maxwell´s equations necessarily involve the continuity equation under the assumption that the displacement current can be ignored. However, in the finite element method, an acceptable solution cannot be obtained if the continuity equation is not treated as an independent equation. The situation is clarified theoretically, and the physical significance is discussed. A model of a conducting liquid in a moving magnetic field is analyzed, and the validity of the proposed formulation is verified by experiment