Electric field just above an interface

I apply a static electric field across a 2D air gap.

Somewhere in the air gal I place a square dielectric. I notice the solved E field is discontinuous at the air-dielectric interface. So it's a different value just inside and just outside the dielectric.

Now I want to plot the E field along one of the edges of the dielectric, just inside or just outside it. I could draw another slightly larger or smaller box around it, and plot E along the edge of this new box, but that tends to mess up my meshing, and I won't get the true boundary values that way. Is there a better way?