Finding potential using poisson's equation, not a homework problem.

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This is not a homework problem. I just want to have a better understanding of scalar electric potential.

In electrostatic, [itex]\; V=-\int_A^B \vec E \cdot \hat{T} dl \;[/itex] where the solution is:

[tex]V=\frac{q}{4\pi \epsilon_0} \frac{1}{B} [/tex]

Where we assume [itex]\; A=\infty[/itex].


At the same time, [itex] \vec E = -\nabla V \Rightarrow \nabla \cdot \nabla \vec E = -\nabla^2 V[/itex].

I want to see whether I can solve V using partial differential equation technique by using:

[tex]V(x,y)=\sum_{m=1}^{\infty} \sum_{n=1}^{\infty} E_{mn} sin(\frac{m\pi}{a}) sin(\frac{n\pi}{b})[/tex]

Where a and b are the boundary condition. My question is how do I set up the boundary condition a and b?
 

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