 #1
happyparticle
 372
 19
 Homework Statement:
 Consider a block of surface ##25cm^2## and thickness 12mm made of lucid a dielectric with ##\epsilon_r = 3.2##. We charge the center of this block with a beam of electron 0.1##\mu A## for 1 second to have a uniform charged layer of 2mm of thickness where the center is at 6mm of the surface of the block.
 Relevant Equations:

##\sigma p = \vec{P} \cdot \hat{n}##
##\vec{P} = \epsilon_0 \chi_e \vec{E} = \frac{\chi_e \vec{D}}{\epsilon_r}##
From what I think, to find the bound charges of a block on the top and bottom surface I have to find the electric field or the displacement (D).
However, I'm not sure how to proceed with a cube. For example, with a sphere ##E = \frac{Q}{4\pi \epsilon_0 r^2}## since r is constant.
For a cube, it depends where I'm at the surface, since the electric field is produce by the charged layer it the center of the cube, r is not the same everywhere on the surface.
Am I correct?
However, I'm not sure how to proceed with a cube. For example, with a sphere ##E = \frac{Q}{4\pi \epsilon_0 r^2}## since r is constant.
For a cube, it depends where I'm at the surface, since the electric field is produce by the charged layer it the center of the cube, r is not the same everywhere on the surface.
Am I correct?