# 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.

## 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?

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.

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?

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

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

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