Dielectric between Grounded Plates

[jmtome2]

Homework Statement

"When a block of insulating material such as Lucite is bombarded with high-energy electrons, the electrons penetrate into the material and remain trapped inside. In one particular instance a 0.1 mA beam bombarded an area of 25cm$$^{2}$$ of Lucite (Class A: $$\epsilon_r$$=3.2) for 1 second, and essentially all the electrons were trapped about 6mm below the surface in a region about 2mm thick. The block is 12mm thick. In the following calculations neglect edge effects and assume a uniform density for the trapped electrons. Assume also that both faces of the Lucite are in contact with grounded conducting plates. Lucite is a Class-A dielectric. What is the bound charge density in the charged region?"

Homework Equations

Gauss' Law

The Attempt at a Solution

Just curious how the grounded plates affect the E field? Can this configuration be treated as a typical parallel capacitor?

 

[jmtome2]

Haven't really dealt with grounded conductors before... this means that extra charge rolls off of these plates leaving them with Q=0, meaning that they don't contribute to the E field?

 

[badphysicist]

Without the grounded conducting plates I would think that you would just take the total number of electrons and divide by the volume of area they are embedded in. With the grounded conducting plates, I would think that you would have to use the mirror method because the electrons would draw positive charge to the plates. The net effect would be to draw some surface charge density maybe that would affect the bound charge density. Those are my thoughts anyway. Also, this wouldn't be a typical parallel capacitor because I don't see any reason for there to be positive charge on one plate and negative on the other. They should have the same (positive) charge on each plate in my opinion.