Charges near a conducting plane

[JSGandora]

Homework Statement

Locate two charges q each and two charges –q each on the corners of a square, with like charges diagonally opposite on another. Show that there are two equipotential surfaces that are planes. In this way obtain, and sketch qualitatively, the field of a single point charge located symmetrically in the inside corner formed by being a metal sheet through a right angle. Which configurations of conducting planes and point charges can be solved this way and which can’t? How about a point charge located on the bisector of a 120° dihedral angle between two conducting planes?

Homework Equations

The Attempt at a Solution

I understand this is an extension of the method of image charges and I think that only conducting planes at 90° to each other can be solved in this way. For the 120° case, the image charges lie on the plane of the two conducting planes and there is no good way to introduce another image charge so that the potential at the planes is constant. Is this correct?

 

[haruspex]

For the 120° case, the image charges lie on the plane of the two conducting planes and there is no good way to introduce another image charge so that the potential at the planes is constant.

That looks right to me.

I think that only conducting planes at 90° to each other can be solved in this way.

No, I believe there are other angles. Which ones won't have the problem you mentioned in respect of 120 degrees?