Visualizing & Solving a 2D Laplace Eq problem (Polar Coordinates)

[majormuss]

Homework Statement

See the attached screenshots for the details and my progress so far.

1)My first question is: Is my picture an accurate rendition of the problem?
2) Am I on the right track with my Boundary Conditions and my first few steps at solving part a)?
Thanks in advance.

Relevant Equations

Laplace Eq.

 

[Chestermiller]

It would be easier if you took the $\theta$ boundary conditions at $-\beta/2$ and $+\beta/2$

 

[majormuss]

It would be easier if you took the $\theta$ boundary conditions at $-\beta/2$ and $+\beta/2$

Thanks, I agree that would make things easier. Is my diagram correct, though? and is everything else correct?