I feel that my recent question could be asked on another SE site, because it's rather about mathematical modelling than about computational side of the simulation. But I don't know what is a better place for it - MO, Math SE, Physics SE? Mathematical Modeling SE is not ready yet. And how should it be asked - as a new question, as a link to the question from here?
Here's my 2 cents on the matter.
In the problem you posed, there was an expectation of what the result should look like, motivated by the science behind the problem. Thus, it makes more sense to diagnose the problem in the following steps:
Verify that your assumptions about the input and outcome are correct.
If correct, check to make sure that the equations and boundary/initial conditions reflect your assumptions.
If both 1. and 2. are correct, then debug the numerical implementation.
In lieu of a mathematical modeling SE site, I recommend posting questions about 1. and 2. in an SE website that most closely matches the science of the problem. In your case, electrostatics would definitely fall into the scope of the Physics SE site.
If your question is more concerned about debugging 3., then the computational science SE site is the right choice.
Of course, this is only my humble opinion. Feel free to point out flaws in my position and propose alternatives :)