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Calculating Multiple Integrals on Mathematica (Electric fields)

 
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Oct11-10, 02:37 PM   #1
 

Calculating Multiple Integrals on Mathematica (Electric fields)

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 Code:
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 Code:
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
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Oct12-10, 06:07 AM   #2
 
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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