Calculating Multiple Integrals on Mathematica (Electric fields)

  1. I'm trying to calculate several stuff about the electric field generated by 2 "plaques"

    My main problem being that in mathematica it calculates fast for a point of the electric field generated in the Y component, but if i try to make the median of all the points in the plaque it takes way to much time.

    And after that i'll have to plot for all the points.


    PHP:
    ax := 0.09
    az := 0.03
    d := 0.052
    V := 3000
    E0 := 8.85 * 10^(-12)
    Ke := 8.9 * 10^9


    Ey1[x_, y_, 0] :=
     Ke * E0 * (V/d) *
      Integrate[((y + d/2) / (((x - x0)^2 + (y + d/2)^2 + z0^2)^(3/2))),
    {x0, -ax/2, ax/2}, {z0, -az/2, az/2}]

    Ey2[x_, y_, 0] :=
     Ke * E0 * (V/d) *
      Integrate[-((y - d/2) / (((x - x0)^2 + (y - d/2)^2 + z0^2)^(3/2))),
    {x0, -ax/2, ax/2}, {z0, -az/2, az/2}]

    Ey[x_, y_, 0] := Ey1[x, y, 0] + Ey2[x, y, 0]

    Eymedio[y_] := (1/ax) * Integrate[Ey[x, y, 0], {x, -ax/2, ax/2}]

    Ey1[0, 0, 0]
    Ey2[0, 0, 0]
    Ey[0, 0, 0]
    Eymedio[0]
    And the output, without Eymedio[0]

    PHP:

    8133.58

    8133.58

    16267.2
     
    so calculating Ey[0,0,0] is fast, but when i try to calculate the "median" it takes like huge time.

    Anything obvious i'm doing wrong with mathematica? i think the formulas are all correct.

    Thanks for help
     
  2. jcsd
  3. That's probably because Ey[0, 0, 0] involves calculating a couple of integrals, while Eymedio[0] involves calculating integrals of integrals.
     
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