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Now that I have a little bit better physical understanding of Poisson’s Equation and the electrostatic potential problem, I tried it again.
∇2 u(r,θ,φ) = q(r,θ,φ)/ε
We have a charged sphere of radius 1 in infinite space:
q = {1 0<r<1 {0 Otherwise
For G(r,r’) = 1/(4π|r-r’|)
u(r) = int_-∞∞ f(r’)G(r,r’)dr’
The results are in the second image. This integral, from my experience only worked when the charge density, q, was a delta function δ(r). Could someone tell me what I’m doing wrong?
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