Laplace's Equation To Find Potential

[baltimorebest]

Homework Statement

Consider a box that has a top and bottom at a/2 and –a/2, while the sides are located at –b/2 and +b/2. Also, the top and bottom are at potential V₀=100V and the sides have V=0. You will need to use the separation of variables technique.

1) Find the general solution using standard methods.
2) Use the given boundary conditions to solve for the solution for this particular geometry.
3) Graph the potential as a function of x/b for y/a=1/2 as a function of y/a for
x/b=0. Also do it for x/b at y/a=0,1/4 and for y/a at x/b=1/2, 1.

Homework Equations

The Attempt at a Solution

I need help with the majority of this problem. My professor gave us the hint of using separation of variables, and she also gave us an example in the book to follow. However, I am still confused on how to do it. As far as the third part of this question, I don't really understand the question. Please help me, and thanks ahead of time.

 

[diazona]

This is very similar (but not quite identical) to the problem being discussed at https://www.physicsforums.com/showthread.php?t=436541, so you might want to follow along there as well.

 

[baltimorebest]

Oh ok. I will follow along and try to post when the other person does. Thanks.

 

[baltimorebest]

I tried to work on this all afternoon and here is what I got for everything except the graphing. I have no idea if it's correct, but I really hope it's close.