Existence of fringe effects with a capacitor

[wimvd]

I was surfing some old exam questions and I found a nasty one... They asked to prove the existence of fringe effects of the electric field at the edges of a plate capacitor, using Maxwell's laws.
In class we always assumed the ideal capacitor without fringe effects so I'm having some kind of mental block. I have no clue what surface or integration path to choose.
The only idea I have is that from a distance the capacitor should look like an electric dipole and show the same field lines as the electric dipole, and thus there should be fringe effects. But that's not really USING Maxwell's laws is it? :/

Any chance someone can put me on the right path/surface?

Thanks.

 

[Manchot]

Probably the easiest argument to make is that the electric field in boundary-less, charge-less, current-less areas must be continuous. Thus, if you move from between the plates to outside the plates, your electric field cannot drop from a finite value to a zero value instantaneously, so there must be some electric field outside the plates.

A more direct application would be to consider a surface that passes through the metal (and encloses some charge), and extends off to infinity. Since the electrix flux through the top and bottom sides of the box must be zero (one is in a metal, one is at infinity), using Gauss's law, there must be some flux going out the sides.

 

[wimvd]

Perfect! Thanks! :)