The discussion revolves around the behavior of an electric field in a dielectric material that contains a cavity when a uniform electric field is applied. Participants explore the implications of the electric displacement field and the continuity conditions at material boundaries, as well as the effects of the cavity on the electric field within it.
Participants express differing views on the behavior of the electric field in the cavity, with no consensus reached on whether the electric field remains null or not.
The discussion includes assumptions about the continuity of electric fields and the implications of charge distribution within the cavity, which may not be fully resolved. The complexity of the problem is acknowledged, with suggestions to explore simpler models for clarity.
Paul Colby said:No, why would one think so? The normal component of ##D=\epsilon(r)E## and the tangent component of ##E## are continuous across dielectric (actually all) material boundaries.
Not if as much ##D## flux exits as enters the volume as leaves which is actually the case. My suggestion is work a 1-D problem that's simple to solve completely. Try a 3 layer parallel plate capacitor with a void layer inside where you ignore fringing fields. Continuity of normal ##D## along with the total voltage drop yields an answer. You will find an ##E\ne0## in the air gap.Leonardo Machado said:But if i close a surface within the hole, there woud not be any charge inside, so ∫ D ⋅ dS = 0 and D = 0.