Electric field and Laplace's equation

[Void123]

Homework Statement

I have to show for a conducting sheet bent along one axis into the shape of a wedge, with a certain angle, that the magnitude of the electric field in the bend is proportional to $$r^{(\pi/\theta) - 1}$$, where theta is the opening angle.

Homework Equations

The Attempt at a Solution

I'm not sure how to treat this problem, is this just separation of variables for Laplace's equation in three dimensions?

 

[nickjer]

You can use separation of variables for Laplace's equation in cylindrical coords. You also know the potential won't have any 'z' dependence so that will simplify your work.

 

[Void123]

I know what the solution is, but I don't really understand the physical logic behind it.

If $$V(s,\phi) = V_{0} + B_{0}Ln s + \Sigma (s^{n}[A cos (n\phi) + B sin (n\phi)] + s^{-n}[C cos (n\phi) + D sin (n\phi)])$$

Now, I know that at z = 0 this forces $$B_{0}, C, and D$$ to go to zero (or else there will be infinite terms), but I don't understand necessarily why. What forces us to conclude, considering cylindrical symmetry, that s -> 0?

 

[nickjer]

Don't forget you have boundary conditions you need to satisfy.

 

[Void123]

Okay, that's what I thought. But which boundary conditions are those if they are not specified in the problem?

 

[nickjer]

They are specified in the problem. What do you know about potentials and conductors.