Regarding governing equations solved in Maxwell-3D eddy current solver

    • kavatar

      Hello Everyone,

      I am trying to understand the governing equations Maxwell-3D uses while calculating magnetic field in different regions.

      I have electromagnetic stirrer set-up having 6-copper coils placed on an iron core. In between these coils, a rotator (steel rod) is placed. In addition, an air enclosure is surrounding this set-up as domain boundary. This setup is just like induction motor. (So I have 4 parts namely; copper coils, iron core, rotator steel rod, and air)

      Excitation: The copper coils are excited with 3-phase AC current. Eddy current is turned on in rotator steel rod only while it is ignored in other parts. Displacement current is also ignored in all parts including air region.

      A screenshot from Maxwell-3D help guide regarding equation being used:

      Doubt-1) How does the above equation in conductor include the effect of external current excitation?


      My problem has 4-regions in which governing equations are: (According to me)


      My doubts are:

      Doubt-2)    What is the governing equation in copper coils? (No eddy and displacement current effects but external current excitation is present)

      Doubt-3)    What will be the governing equation if I turn on the eddy current effects in coil also? (No displacement current but in addition to external current excitation eddy current effects are on in coil)

      Doubt-4)    Can anyone confirm if the governing equation which I wrote in iron-core is correct? As this is conducting medium without eddy current, displacement current and without external current source

      Also, could anyone please suggest a paper where I can get detailed explaination of eddy current solve in 3D?




    • Navya C
      Ansys Employee


      Hi Kavatar,

      Equations necessary for a user’s understanding have been provided in the help file.

      Additional information on solver details may depend on your application and require detailed discussion.

      There may be information that we cannot share in a public forum.

      I suggested you submit a service request(SR) with Ansys customer support.


    • kavatar

      Thanks Navya C for responding.

      I didn't reply back to the tread because I was reading research papers to get more clearity. I also read Maxwell3D technical note part in the manual in detail. I have got one very basic query, and hoping your clarification on that.

      In the manual the H is defined in the following way: 

      And later, following governing equations are listed for H: 

      As per my understanding Hp is magnetic field due to source current, T is electric vector potential defined in the conducting region with eddy current turned on, and both Ω and φ represent the magnetic scalar potential. 

      Could you please tell what is the difference between the definition of Ω and φ?

      Are these related to reduced magnetic scalar potential and total magnetic scalar potential?  

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