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[✓] Entity throws a set:tag inactive in (....)[..] is protected, ...

GROUPS:

Hi, Entity throws a set:tag inactive in (....)[..] is protected, but ReleaseHold[WolframAlpha[...] is not. I am wondering why. I am following Michael Trott blog at: http://blog.wolfram.com/data/uploads/2013/08/MusingMagnets.cdf He is getting curated data into the notebook by using WolframAlpha:

\[Psi]BarMagnetHeld  = 
  WolframAlpha[
   "magnetic potential rectangular bar magnet", {{"Result", 1}, 
    "Input"}];

(* magnetic potential *)
\[Psi]BarMagnet[{x_, y_, z_}, {a_, b_, c_}] =
   ReleaseHold[\[Psi]BarMagnetHeld]/Subscript[M, 0];

His output from the second input looks like this:

-(1/(4 \[Pi]))(((-(a/2) - x) (-(b/2) - y))/
   Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] - ((a/2 - 
      x) (-(b/2) - y))/
   Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] - ((-(a/2) - 
      x) (b/2 - y))/
   Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + ((a/2 - 
      x) (b/2 - y))/
   Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - 
      z)^2] - ((-(a/2) - 
        x) ((-(a/2) - x)^2 + (-(b/2) - y)^2) (-(b/2) - 
        y)^3)/(2 ((-(b/2) - 
           y)^2 ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^(
         3/2) + (-(a/2) - 
           x)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - 
            z)^2] (-(c/2) - z)^2)) - ((-(a/2) - 
        x)^3 ((-(a/2) - x)^2 + (-(b/2) - y)^2) (-(b/2) - 
        y))/(2 ((-(a/2) - 
           x)^2 ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^(
         3/2) + (-(b/2) - 
           y)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - 
            z)^2] (-(c/2) - z)^2)) + ((a/2 - 
        x) ((a/2 - x)^2 + (-(b/2) - y)^2) (-(b/2) - 
        y)^3)/(2 ((-(b/2) - 
           y)^2 ((a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^(
         3/
          2) + (a/2 - 
           x)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - 
            z)^2] (-(c/2) - z)^2)) + ((a/2 - 
        x)^3 ((a/2 - x)^2 + (-(b/2) - y)^2) (-(b/2) - 
        y))/(2 ((a/2 - 
           x)^2 ((a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^(
         3/2) + (-(b/2) - 
           y)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - 
            z)^2] (-(c/2) - z)^2)) + ((-(a/2) - 
        x) ((-(a/2) - x)^2 + (b/2 - y)^2) (b/2 - 
        y)^3)/(2 ((b/2 - 
           y)^2 ((-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^(
         3/2) + (-(a/2) - 
           x)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - 
            z)^2] (-(c/2) - z)^2)) + ((-(a/2) - 
        x)^3 ((-(a/2) - x)^2 + (b/2 - y)^2) (b/2 - 
        y))/(2 ((-(a/2) - 
           x)^2 ((-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^(
         3/2) + (b/2 - 
           y)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - 
            z)^2] (-(c/2) - z)^2)) - ((a/2 - 
        x) ((a/2 - x)^2 + (b/2 - y)^2) (b/2 - 
        y)^3)/(2 ((b/2 - 
           y)^2 ((a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^(
         3/2) + (a/2 - 
           x)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/
            2) - z)^2)) - ((a/2 - x)^3 ((a/2 - x)^2 + (b/2 - y)^2) (b/
        2 - y))/(2 ((a/2 - 
           x)^2 ((a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^(
         3/2) + (b/2 - 
           y)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/
            2) - z)^2)) - ((-(a/2) - x) (-(b/2) - y))/
   Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + ((a/2 - 
      x) (-(b/2) - y))/
   Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + ((-(a/2) - 
      x) (b/2 - y))/
   Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] - ((a/2 - x) (b/
      2 - y))/Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - 
      z)^2] + ((-(a/2) - 
        x) ((-(a/2) - x)^2 + (-(b/2) - y)^2) (-(b/2) - 
        y)^3)/(2 ((-(b/2) - 
           y)^2 ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^(
         3/2) + (-(a/2) - 
           x)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - 
            z)^2] (c/2 - z)^2)) + ((-(a/2) - 
        x)^3 ((-(a/2) - x)^2 + (-(b/2) - y)^2) (-(b/2) - 
        y))/(2 ((-(a/2) - 
           x)^2 ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^(
         3/2) + (-(b/2) - 
           y)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - 
            z)^2] (c/2 - z)^2)) - ((a/2 - 
        x) ((a/2 - x)^2 + (-(b/2) - y)^2) (-(b/2) - 
        y)^3)/(2 ((-(b/2) - 
           y)^2 ((a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^(
         3/2) + (a/2 - 
           x)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/
           2 - z)^2)) - ((a/2 - 
        x)^3 ((a/2 - x)^2 + (-(b/2) - y)^2) (-(b/2) - 
        y))/(2 ((a/2 - 
           x)^2 ((a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^(
         3/2) + (-(b/2) - 
           y)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/
           2 - z)^2)) - ((-(a/2) - 
        x) ((-(a/2) - x)^2 + (b/2 - y)^2) (b/2 - 
        y)^3)/(2 ((b/2 - 
           y)^2 ((-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^(
         3/2) + (-(a/2) - 
           x)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/
           2 - z)^2)) - ((-(a/2) - 
        x)^3 ((-(a/2) - x)^2 + (b/2 - y)^2) (b/2 - 
        y))/(2 ((-(a/2) - 
           x)^2 ((-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^(
         3/2) + (b/2 - 
           y)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/
           2 - z)^2)) + ((a/2 - x) ((a/2 - x)^2 + (b/2 - y)^2) (b/2 - 
        y)^3)/(2 ((b/2 - 
           y)^2 ((a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^(
         3/2) + (a/2 - 
           x)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/2 - 
           z)^2)) + ((a/2 - x)^3 ((a/2 - x)^2 + (b/2 - y)^2) (b/2 - 
        y))/(2 ((a/2 - 
           x)^2 ((a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^(
         3/2) + (b/2 - 
           y)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/2 - 
           z)^2)) + ((-(b/2) - y) (-(c/2) - z)^2)/((-(a/2) - 
      x)^2 + (-(b/2) - 
      y)^2 + (-(a/2) - 
       x) Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + (-(
       c/2) - z)^2) + ((-(a/2) - x) (-(c/2) - z)^2)/((-(a/2) - 
      x)^2 + (-(b/2) - 
      y)^2 + (-(b/2) - 
       y) Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + (-(
       c/2) - z)^2) - ((-(b/2) - y) (-(c/2) - z)^2)/((a/2 - 
      x)^2 + (-(b/2) - 
      y)^2 + (a/2 - 
       x) Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + (-(c/
       2) - z)^2) - ((a/2 - x) (-(c/2) - z)^2)/((a/2 - 
      x)^2 + (-(b/2) - 
      y)^2 + (-(b/2) - 
       y) Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] + (-(c/
       2) - z)^2) - ((b/2 - y) (-(c/2) - z)^2)/((-(a/2) - x)^2 + (b/
      2 - y)^2 + (-(a/2) - 
       x) Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + (-(c/
       2) - z)^2) - ((-(a/2) - x) (-(c/2) - z)^2)/((-(a/2) - 
      x)^2 + (b/2 - 
      y)^2 + (b/2 - 
       y) Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + (-(c/
       2) - z)^2) + ((b/2 - y) (-(c/2) - z)^2)/((a/2 - x)^2 + (b/2 - 
      y)^2 + (a/2 - 
       x) Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + (-(c/2) -
       z)^2) + ((a/2 - x) (-(c/2) - z)^2)/((a/2 - x)^2 + (b/2 - 
      y)^2 + (b/2 - 
       y) Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] + (-(c/2) -
       z)^2) + ((-(a/2) - x) (-(b/2) - 
        y) ((-(a/2) - x)^2 + (-(b/2) - y)^2 + 
        2 (-(c/2) - z)^2) (-(c/2) - 
        z)^2)/(2 ((-(a/2) - x)^2 (-(b/2) - 
           y)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - 
            z)^2] + ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - 
             z)^2)^(3/2) (-(c/2) - z)^2)) - ((a/2 - x) (-(b/2) - 
        y) ((a/2 - x)^2 + (-(b/2) - y)^2 + 2 (-(c/2) - z)^2) (-(c/2) -
         z)^2)/(2 ((a/2 - x)^2 (-(b/2) - 
           y)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - 
            z)^2] + ((a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2)^(
         3/2) (-(c/2) - z)^2)) - ((-(a/2) - x) (b/2 - 
        y) ((-(a/2) - x)^2 + (b/2 - y)^2 + 2 (-(c/2) - z)^2) (-(c/2) -
         z)^2)/(2 ((-(a/2) - x)^2 (b/2 - 
           y)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - 
            z)^2] + ((-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^(
         3/2) (-(c/2) - z)^2)) + ((a/2 - x) (b/2 - 
        y) ((a/2 - x)^2 + (b/2 - y)^2 + 2 (-(c/2) - z)^2) (-(c/2) - 
        z)^2)/(2 ((a/2 - x)^2 (b/2 - 
           y)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - 
            z)^2] + ((a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2)^(
         3/2) (-(c/2) - z)^2)) - ((-(b/2) - y) (c/2 - z)^2)/((-(a/2) -
       x)^2 + (-(b/2) - 
      y)^2 + (-(a/2) - 
       x) Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + (c/2 -
       z)^2) - ((-(a/2) - x) (c/2 - z)^2)/((-(a/2) - x)^2 + (-(b/2) - 
      y)^2 + (-(b/2) - 
       y) Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + (c/2 -
       z)^2) + ((-(b/2) - y) (c/2 - z)^2)/((a/2 - x)^2 + (-(b/2) - 
      y)^2 + (a/2 - 
       x) Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + (c/2 - 
      z)^2) + ((a/2 - x) (c/2 - z)^2)/((a/2 - x)^2 + (-(b/2) - 
      y)^2 + (-(b/2) - 
       y) Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] + (c/2 - 
      z)^2) + ((b/2 - y) (c/2 - z)^2)/((-(a/2) - x)^2 + (b/2 - 
      y)^2 + (-(a/2) - 
       x) Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + (c/2 - 
      z)^2) + ((-(a/2) - x) (c/2 - z)^2)/((-(a/2) - x)^2 + (b/2 - 
      y)^2 + (b/2 - 
       y) Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + (c/2 - 
      z)^2) - ((b/2 - y) (c/2 - z)^2)/((a/2 - x)^2 + (b/2 - 
      y)^2 + (a/2 - 
       x) Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + (c/2 - 
      z)^2) - ((a/2 - x) (c/2 - z)^2)/((a/2 - x)^2 + (b/2 - 
      y)^2 + (b/2 - 
       y) Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] + (c/2 - 
      z)^2) - ((-(a/2) - x) (-(b/2) - 
        y) ((-(a/2) - x)^2 + (-(b/2) - y)^2 + 2 (c/2 - z)^2) (c/2 - 
        z)^2)/(2 ((-(a/2) - x)^2 (-(b/2) - 

           y)^2 Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - 
            z)^2] + ((-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^(
         3/2) (c/2 - z)^2)) + ((a/2 - x) (-(b/2) - 
        y) ((a/2 - x)^2 + (-(b/2) - y)^2 + 2 (c/2 - z)^2) (c/2 - 
        z)^2)/(2 ((a/2 - x)^2 (-(b/2) - 
           y)^2 Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - 
            z)^2] + ((a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2)^(
         3/2) (c/2 - z)^2)) + ((-(a/2) - x) (b/2 - 
        y) ((-(a/2) - x)^2 + (b/2 - y)^2 + 2 (c/2 - z)^2) (c/2 - 
        z)^2)/(2 ((-(a/2) - x)^2 (b/2 - 
           y)^2 Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - 
            z)^2] + ((-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^(
         3/2) (c/2 - z)^2)) - ((a/2 - x) (b/2 - 
        y) ((a/2 - x)^2 + (b/2 - y)^2 + 2 (c/2 - z)^2) (c/2 - 
        z)^2)/(2 ((a/2 - x)^2 (b/2 - 
           y)^2 Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - 
            z)^2] + ((a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2)^(
         3/2) (c/2 - z)^2)) - (-(c/2) - 
      z) ArcTan[((-(a/2) - x) (-(b/2) - y))/(
     Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] (-(c/2) - 
        z))] + (-(c/2) - z) ArcTan[((a/2 - x) (-(b/2) - y))/(
     Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2] (-(c/2) - 
        z))] + (-(c/2) - z) ArcTan[((-(a/2) - x) (b/2 - y))/(
     Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/2) - 
        z))] - (-(c/2) - z) ArcTan[((a/2 - x) (b/2 - y))/(
     Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2] (-(c/2) - 
        z))] + (c/2 - z) ArcTan[((-(a/2) - x) (-(b/2) - y))/(
     Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/2 - 
        z))] - (c/2 - z) ArcTan[((a/2 - x) (-(b/2) - y))/(
     Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2] (c/2 - 
        z))] - (c/2 - z) ArcTan[((-(a/2) - x) (b/2 - y))/(
     Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/2 - 
        z))] + (c/2 - z) ArcTan[((a/2 - x) (b/2 - y))/(
     Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2] (c/2 - z))] + (-(b/
       2) - y) Log[-(a/2) - x + 
      Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2]] + (-(a/
       2) - x) Log[-(b/2) - y + 
      Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2]] - (-(b/
       2) - y) Log[
     a/2 - x + 
      Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2]] - (a/2 - 
      x) Log[-(b/2) - y + 
      Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (-(c/2) - z)^2]] - (b/2 - 
      y) Log[-(a/2) - x + 
      Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2]] - (-(a/2) -
       x) Log[b/2 - y + 
      Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2]] + (b/2 - 
      y) Log[a/2 - x + 
      Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2]] + (a/2 - 
      x) Log[b/2 - y + 
      Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (-(c/2) - z)^2]] - (-(b/2) - 
      y) Log[-(a/2) - x + 
      Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2]] - (-(a/2) -
       x) Log[-(b/2) - y + 
      Sqrt[(-(a/2) - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2]] + (-(b/2) -
       y) Log[a/2 - x + 
      Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2]] + (a/2 - 
      x) Log[-(b/2) - y + 
      Sqrt[(a/2 - x)^2 + (-(b/2) - y)^2 + (c/2 - z)^2]] + (b/2 - 
      y) Log[-(a/2) - x + 
      Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2]] + (-(a/2) - 
      x) Log[
     b/2 - y + Sqrt[(-(a/2) - x)^2 + (b/2 - y)^2 + (c/2 - z)^2]] - (b/
      2 - y) Log[
     a/2 - x + Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2]] - (a/2 -
       x) Log[b/2 - y + 
      Sqrt[(a/2 - x)^2 + (b/2 - y)^2 + (c/2 - z)^2]])

without any warnings. I am trying to do the same but without WolframAlpha.

In[65]:= rbmmsp[{x_, y_, z_}, {a_, b_, c_}] = 
 Entity["PhysicalSystem", "RectangularBarMagnet"][
   "MagneticScalarPotential"]/Subscript[M, 0]

During evaluation of In[65]:= Set::write: Tag Inactive in (-((Subscript[M, 0] (Log[Subscript[y, m]+Subscript[r, 1,1,1]] Subscript[x, m]-Log[Subscript[y, m]+Subscript[r, 1,1,2]] Subscript[x, m]-Log[Subscript[y, p]+Subscript[r, <<1>>]] Subscript[x, m]+<<71>>+<<22>>))/(4 \[Pi]))//.{Subscript[x, m]:>-(a/2)-x,Subscript[x, p]:>a/2-x,Subscript[y, m]:>-(b/2)-y,Subscript[y, p]:>b/2-y,<<7>>,Subscript[r, 2,1,2]:>Sqrt[\!\(\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)] + \*SubsuperscriptBox[\("y"\), \("m"\), \(2\)] + \*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\)],Subscript[r, 2,2,1]:>Sqrt[\!\(\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)] + \*SubsuperscriptBox[\("y"\), \("p"\), \(2\)] + \*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\)],Subscript[r, 2,2,2]:>Sqrt[\!\(\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)] + \*SubsuperscriptBox[\("y"\), \("p"\), \(2\)] + \*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\)]})[{x_,y_,z_},{a_,b_,c_}] is Protected.

Out[65]= 1/Subscript[M, 0] (-(1/(4 \[Pi]))
    QuantityVariable[Subscript["M", 0],"Magnetization"] (Log[
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) + Subscript["r", 1, 1, 1]] 
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) - Log[
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) + Subscript["r", 1, 1, 2]] 
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) - Log[
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) + Subscript["r", 1, 2, 1]] 
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) + Log[
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) + Subscript["r", 1, 2, 2]] 
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) - Log[
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) + Subscript["r", 2, 1, 1]] 
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) + Log[
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) + Subscript["r", 2, 1, 2]] 
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) + Log[
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) + Subscript["r", 2, 2, 1]] 
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) - Log[
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) + Subscript["r", 2, 2, 2]] 
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) + Log[
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) + Subscript["r", 1, 1, 1]] 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) - Log[
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) + Subscript["r", 1, 1, 2]] 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) - Log[
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) + Subscript["r", 2, 1, 1]] 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) + Log[
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) + Subscript["r", 2, 1, 2]] 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) - Log[
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) + Subscript["r", 1, 2, 1]] 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) + Log[
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) + Subscript["r", 1, 2, 2]] 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) + Log[
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) + Subscript["r", 2, 2, 1]] 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) - Log[
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) + Subscript["r", 2, 2, 2]] 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) - ArcTan[(
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\))/(
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) Subscript["r", 1, 1, 1])] 
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) + ArcTan[(
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\))/(
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) Subscript["r", 1, 2, 1])] 
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) + ArcTan[(
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\))/(
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) Subscript["r", 2, 1, 1])] 
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) - ArcTan[(
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\))/(
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) Subscript["r", 2, 2, 1])] 
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) + ArcTan[(
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\))/(
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) Subscript["r", 1, 1, 2])] 
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) - ArcTan[(
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\))/(
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) Subscript["r", 1, 2, 2])] 
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) - ArcTan[(
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\))/(
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) Subscript["r", 2, 1, 2])] 
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) + ArcTan[(
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\))/(
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) Subscript["r", 2, 2, 2])] 
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) + (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\))/Subscript["r", 1, 1, 1] + (
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) Subscript["r", 1, 1, 1] + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 1, 1\), \(2\)]\)) + (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) Subscript["r", 1, 1, 1] + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 1, 1\), \(2\)]\)) - (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(3\)]\ 
\*SubscriptBox[\("y"\), \("m"\)]\ \((\(-
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) + 
\*SubsuperscriptBox[\("r"\), \(1, 1, 1\), \(2\)])\)\))/(2 (\!\(
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 1, 1\)]\) + \!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 1, 1\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("y"\), \("m"\), \(3\)]\) (-
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 1, 1\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 1, 1\)]\) + \!\(
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 1, 1\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("r"\), \(1, 1, 1\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 1, 1\)]\) + \!\(
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 1, 1\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\))/Subscript["r", 1, 1, 2] - (
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) Subscript["r", 1, 1, 2] + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 1, 2\), \(2\)]\)) - (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) Subscript["r", 1, 1, 2] + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 1, 2\), \(2\)]\)) + (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(3\)]\ 
\*SubscriptBox[\("y"\), \("m"\)]\ \((\(-
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) + 
\*SubsuperscriptBox[\("r"\), \(1, 1, 2\), \(2\)])\)\))/(2 (\!\(
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 1, 2\)]\) + \!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 1, 2\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("y"\), \("m"\), \(3\)]\) (-
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 1, 2\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 1, 2\)]\) + \!\(
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 1, 2\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("r"\), \(1, 1, 2\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 1, 2\)]\) + \!\(
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 1, 2\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\))/Subscript["r", 1, 2, 1] - (
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) Subscript["r", 1, 2, 1] + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 2, 1\), \(2\)]\)) - (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) Subscript["r", 1, 2, 1] + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 2, 1\), \(2\)]\)) + (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(3\)]\ 
\*SubscriptBox[\("y"\), \("p"\)]\ \((\(-
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) + 
\*SubsuperscriptBox[\("r"\), \(1, 2, 1\), \(2\)])\)\))/(2 (\!\(
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 2, 1\)]\) + \!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 2, 1\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("y"\), \("p"\), \(3\)]\) (-
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 2, 1\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 2, 1\)]\) + \!\(
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 2, 1\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("r"\), \(1, 2, 1\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 2, 1\)]\) + \!\(
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 2, 1\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\))/Subscript["r", 1, 2, 2] + (
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) Subscript["r", 1, 2, 2] + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 2, 2\), \(2\)]\)) + (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) Subscript["r", 1, 2, 2] + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 2, 2\), \(2\)]\)) - (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(3\)]\ 
\*SubscriptBox[\("y"\), \("p"\)]\ \((\(-
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) + 
\*SubsuperscriptBox[\("r"\), \(1, 2, 2\), \(2\)])\)\))/(2 (\!\(
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 2, 2\)]\) + \!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 2, 2\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("y"\), \("p"\), \(3\)]\) (-
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) + 
\!\(\*SubsuperscriptBox[\("r"\), \(1, 2, 2\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 2, 2\)]\) + \!\(
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 2, 2\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("r"\), \(1, 2, 2\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(1, 2, 2\)]\) + \!\(
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(1, 2, 2\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\))/Subscript["r", 2, 1, 1] - (
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) Subscript["r", 2, 1, 1] + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 1, 1\), \(2\)]\)) - (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) Subscript["r", 2, 1, 1] + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 1, 1\), \(2\)]\)) + (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(3\)]\ 
\*SubscriptBox[\("y"\), \("m"\)]\ \((\(-
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) + 
\*SubsuperscriptBox[\("r"\), \(2, 1, 1\), \(2\)])\)\))/(2 (\!\(
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 1, 1\)]\) + \!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 1, 1\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("y"\), \("m"\), \(3\)]\) (-
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 1, 1\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 1, 1\)]\) + \!\(
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 1, 1\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("r"\), \(2, 1, 1\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 1, 1\)]\) + \!\(
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 1, 1\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\))/Subscript["r", 2, 1, 2] + (
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) Subscript["r", 2, 1, 2] + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 1, 2\), \(2\)]\)) + (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) Subscript["r", 2, 1, 2] + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 1, 2\), \(2\)]\)) - (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(3\)]\ 
\*SubscriptBox[\("y"\), \("m"\)]\ \((\(-
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) + 
\*SubsuperscriptBox[\("r"\), \(2, 1, 2\), \(2\)])\)\))/(2 (\!\(
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 1, 2\)]\) + \!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 1, 2\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("y"\), \("m"\), \(3\)]\) (-
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 1, 2\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 1, 2\)]\) + \!\(
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 1, 2\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("r"\), \(2, 1, 2\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 1, 2\)]\) + \!\(
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 1, 2\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\))/Subscript["r", 2, 2, 1] + (
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) Subscript["r", 2, 2, 1] + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 2, 1\), \(2\)]\)) + (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) Subscript["r", 2, 2, 1] + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 2, 1\), \(2\)]\)) - (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(3\)]\ 
\*SubscriptBox[\("y"\), \("p"\)]\ \((\(-
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) + 
\*SubsuperscriptBox[\("r"\), \(2, 2, 1\), \(2\)])\)\))/(2 (\!\(
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 2, 1\)]\) + \!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 2, 1\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("y"\), \("p"\), \(3\)]\) (-
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 2, 1\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 2, 1\)]\) + \!\(
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 2, 1\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("r"\), \(2, 2, 1\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 2, 1\)]\) + \!\(
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 2, 1\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\))/Subscript["r", 2, 2, 2] - (
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) Subscript["r", 2, 2, 2] + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 2, 2\), \(2\)]\)) - (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\))/(
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) Subscript["r", 2, 2, 2] + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 2, 2\), \(2\)]\)) + (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(3\)]\ 
\*SubscriptBox[\("y"\), \("p"\)]\ \((\(-
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) + 
\*SubsuperscriptBox[\("r"\), \(2, 2, 2\), \(2\)])\)\))/(2 (\!\(
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 2, 2\)]\) + \!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 2, 2\), \(3\)]\))) + (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("y"\), \("p"\), \(3\)]\) (-
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) + 
\!\(\*SubsuperscriptBox[\("r"\), \(2, 2, 2\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 2, 2\)]\) + \!\(
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 2, 2\), \(3\)]\))) - (
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) 
\!\(\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\) (\!\(
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("r"\), \(2, 2, 2\), \(2\)]\)))/(2 (\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)]\ 
\*SubscriptBox[\("r"\), \(2, 2, 2\)]\) + \!\(
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\ 
\*SubsuperscriptBox[\("r"\), \(2, 2, 2\), \(3\)]\)))) \!\(\*
TagBox["//.",
"InactiveToken",
BaseStyle->"Inactive",
SyntaxForm->"//."]\) {
\!\(\*SubscriptBox[\("x"\), \("m"\)]\) :> -(QuantityVariable[
       "a","Length"]/2) - QuantityVariable["x","Length"], 
\!\(\*SubscriptBox[\("x"\), \("p"\)]\) :> 
     QuantityVariable["a","Length"]/2 - QuantityVariable[
      "x","Length"], 
\!\(\*SubscriptBox[\("y"\), \("m"\)]\) :> -(QuantityVariable[
       "b","Length"]/2) - QuantityVariable["y","Length"], 
\!\(\*SubscriptBox[\("y"\), \("p"\)]\) :> 
     QuantityVariable["b","Length"]/2 - QuantityVariable[
      "y","Length"], 
\!\(\*SubscriptBox[\("z"\), \("m"\)]\) :> -(QuantityVariable[
       "c","Length"]/2) - QuantityVariable["z","Length"], 
\!\(\*SubscriptBox[\("z"\), \("p"\)]\) :> 
     QuantityVariable["c","Length"]/2 - QuantityVariable[
      "z","Length"], Subscript["r", 1, 1, 1] :> Sqrt[\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\)], 
    Subscript["r", 1, 1, 2] :> Sqrt[\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\)], 
    Subscript["r", 1, 2, 1] :> Sqrt[\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\)], 
    Subscript["r", 2, 1, 1] :> Sqrt[\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\)], 
    Subscript["r", 1, 2, 2] :> Sqrt[\!\(
\*SubsuperscriptBox[\("x"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\)], 
    Subscript["r", 2, 1, 2] :> Sqrt[\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("y"\), \("m"\), \(2\)] + 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\)], 
    Subscript["r", 2, 2, 1] :> Sqrt[\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("z"\), \("m"\), \(2\)]\)], 
    Subscript["r", 2, 2, 2] :> Sqrt[\!\(
\*SubsuperscriptBox[\("x"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("y"\), \("p"\), \(2\)] + 
\*SubsuperscriptBox[\("z"\), \("p"\), \(2\)]\)]})

and I am getting the warning.
How can I avoid it? Thanks ahead, János

POSTED BY: Janos Lobb
Answer
11 months ago

Let's look at the output of

Entity["PhysicalSystem",  "RectangularBarMagnet"]["MagneticScalarPotential"]

The output will look fairly normal, but if you inspect it closely, you'll notice two things.

(1) "Subscript[M, 0]" is not actually a simple variable. Mouse over it. It's a "QuantityVariable". More specifically it's actually:

QuantityVariable[Subscript["M", 0], "Magnetization"]

You need to divide by that and not Subscript[M, 0].

(2) The expression contains Inactivate. Inactivate is a more modern way of stoping something from evaluating than using Hold. Use Activate to remove the Inactivations.

Activate[Entity["PhysicalSystem", "RectangularBarMagnet"]["MagneticScalarPotential"]/QuantityVariable[Subscript["M", 0],"Magnetization"]]
POSTED BY: Sean Clarke
Answer
11 months ago

Hi Sean,

I saw the HoldComplete[ReleaseHold[Hold[... ] construct and the ReleaseHold[...] on the result when executed Michael's code in Mathematica, so I also tried ReleaseHold[...] on the Entity[...] line, but it did not worked. Of course now Activate[...] with the QuantityVariable[Subscript["M", 0],"Magnetization"]] is working and the two outputs are the same, so I can continue with me study of his blog. Thanks a lot, János

POSTED BY: Janos Lobb
Answer
11 months ago

Group Abstract Group Abstract