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Physics: Insulating material bombarded with electrons. What is bound charge density?

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In pdf format, please provide the following, the derivations of formulae. I will draw all the sketches myself:

When a block of insulating material such as Lucite is bombarded with electrons, the electrons penetrate into the material and remain trapped inside. In one particular instance a 0.1 microampere beam bombarded an area of 25 square cm of Lucite (epsilon-sub-r = 3.2) for 1 second, and essentially all the electrons were trapped about 6 mm below the surface in a region about 2mm thick. the block was 12 mm thick.

Neglect edge effects and assume uniform density for trapped electrons. Also assume both faces of lucite are in contact with grounding plates.

a. What is the bound charge density in the charged region?

b. What is the bound charge density at the surface of the Lucite?

c. Sketch graphs of D, E, V, as functions of position inside the dielectric

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Solution Summary

This solution derives the formula with explanation in an attached PDF document. Graphs are not included. Bounded charge density is examined for insulated material bombarded with electrons.