Calculating Multiple Integrals on Mathematica (Electric fields)

[GriffinHeart]

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.

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]

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

 

[arkajad]

That's probably because Ey[0, 0, 0] involves calculating a couple of integrals, while Eymedio[0] involves calculating integrals of integrals.