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

#### yungman

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

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

$$V=\frac{q}{4\pi \epsilon_0} \frac{1}{B}$$

Where we assume $\; A=\infty$.

At the same time, $\vec E = -\nabla V \Rightarrow \nabla \cdot \nabla \vec E = -\nabla^2 V$.

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

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

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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