I have a quick question about solving Laplace's equation for a wedge with radius a and angle 60º. I need to make the periodicity conditions correctly, so that I can have a reasonable problem to solve. For a circular ring you would simply say that the equation should not differ whether you come from the top or bottom, so that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]u (r, \pi) = u(r, -\pi)[/tex]

for which the rates would have to be the same too

[tex]\frac{\partial u}{\partial \theta} (r, \pi) = \frac{\partial u}{\partial \theta} (r, -\pi)[/tex]

So, this is good because these periodicity conditions give the eigenfunctions

[tex]sin n\theta[/tex] and [tex] cos n \theta[/tex]

My question is whether this still holds for the wedge. Obviously anywhere on the circle it all still applies, but what about the radial parts of the wedge? Should those be treated with their own periodicity conditions? If so, would it just be that

u(r, 0) = u(r, pi/3)

But that worries me if it is so because that won't give nice eigenvalues and eigenfunctions for the radial parts.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Laplace's eqn of wedge

**Physics Forums | Science Articles, Homework Help, Discussion**