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# F16 PH333 4.4.1-4.4.4

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## Richard Datwyler

on 6 November 2018

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#### Transcript of F16 PH333 4.4.1-4.4.4

Linear Dielectrics

4.4.1 Dielectric constant
4.4.2 Boundary value problems
4.4.3 Energy
4.4.4 Forces
Dielectric Constant
Dielectric constant
from 4.1 we know that polarization can come from E fields
note this is for linear dielectrics
Easier to get E by starting with D
with epsilon as the dielectric constant defined by
Putting those two together gives
But we almost always deal with potentials
If the boundary is between dielectric and free space (free space above, dielectric below)
Collecting ideas
This kills of B term inside
This links A and B on boundary
if sigma_f is zero
this links A and B on boundary
set V = 0 at object equator
Kills off all but 1
A term outside
here chi is called electric susceptibility
The is the total permittivity, and the er is the relative permittivity or dielectric constant.
as we consider E and P and D
we still have issues with curls and Boundaries
Following Stokes theorem and a line integral across a boundary gives the important results
from a point charge
E field in a dielectric has this value
Energy in Dielectric System
From chapter 2 we had a definition of energy, with a slight change we can account for the electric displacement part
There is a bit of a proof, but I'll leave that to you.
Forces on dielectrics

due to fringe field effects and bound charges being induced on the surface of the dielectric there will be a force pulling a dielectric into a capacitor of this value.
With C being
d
l
w
x
I'm still not clear on why we don't need to worry about the fringing field
Though bound charges contribute to the electric displacement value, why do we only need to know the free charges to calculate D?
I am not following much of the material. Can you describe permittivity, susceptibility. what do they mean?
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