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

  • Thread starter yungman
  • Start date
4,235
39
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?
 

Want to reply to this thread?

"Finding potential using poisson's equation, not a homework problem." You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads

Top