I am new to Mathematica and I am trying to automate the process of finding electric and magnetic fields for TE and TM modes in a cylindrical superconducting cavity. I could not find documentation through which I can define a vector field.

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    $\begingroup$ A vector field should be just a list of functions. So, for instance, f[x_, y_] = {-y, x} would correspond to the vector field $r \hat{\phi}$, where the two elements of the list are the Cartesian components written in Cartesian coordinates. $\endgroup$
    – march
    Feb 6, 2022 at 21:41
  • $\begingroup$ Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. $\endgroup$
    – bbgodfrey
    Feb 6, 2022 at 23:56
  • $\begingroup$ Have a look at:" mathematica.stackexchange.com/questions/173081/…". This is for spherical coordinates, but cylindrical coordinates are simpler. $\endgroup$ Feb 7, 2022 at 9:26


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