Cavity in a dielectric material

[Leonardo Machado]

Hello friends.

If i have a dieletric material ( w/ a hole) and apply an uniform eletric field on it, the eletric field in the hole will stay null ?

Peace.

 

[Paul Colby]

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.

 

[Leonardo Machado]

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.

But if i close a surface within the hole, there woud not be any charge inside, so ∫ D ⋅ dS = 0 and D = 0.

 

[Paul Colby]

But if i close a surface within the hole, there woud not be any charge inside, so ∫ D ⋅ dS = 0 and D = 0.

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.