Edge Effect in Parallel Plate Capacitors I have a problem understanding the edge effect in parallel plate capacitors. The part of the fringe is clear to me, at least I think so. I know that the field fringes to the outside of the capacitor, therefore decreasing the field inside the capacitor at the edges. But what I do not understand is the singularity which arises at the electrode edge. If I take a look at these edges in a finite element simulation, the results look often as shown in this picture

Here the source just to be consistent
So here is my problem. These edges clearly contain singularities, but I do not understand the physical mechanism behind it. Can someone provide some insight into this problem? I tried studying the boundary conditions between a conductor and a dielectric, but all I got was that the change in the normal component of the dielectric displacement field equals the surface charge density. And I do not see why this is singular at the edges...
Regards
Philipp
 A: To complete the previous answer, I propose to look first at a charged wire of a finite length. The charge density will not be distributed uniformly, but will have maxima at the wire ends. 
If we place a similar wrie parallel to the first one, but charged oppositely, the maxima will be smaller, but still present. 
If the wires or capacitor plates are not infinitely thin, there will not be true singularities, but maxima instead.
A: Here is one way of looking at it which may help. 
We begin with a sphere upon which there exists a uniform charge density. The density of the field lines (that is, field lines per square cm of surface) extending away from the sphere into space will have some value. Now we magically shrink the sphere, without allowing any of the charge to escape, and discover that if we reduce the area of the sphere by half, we have doubled the density of the field lines at its surface. We continue this process of shrinking the sphere and find that as the radius of the sphere goes to zero, the intensity of the field (measured by the density of the field lines) at its surface tends towards infinity. 
From this we conclude that if there is a physical singularity (an infinitely sharp edge or a needle-sharp point) on a charged surface, then the electric field at that point or edge will tend to develop a singularity there too. 
