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F16 PH 333 4.3.1-4.4.1
Transcript of F16 PH 333 4.3.1-4.4.1
4.3.1 Gauss's Law with Dielectrics
4.3.3 Boundary Conditions
4.4.1 Dielectric Constant
Gauss's Law with Dielectrics
Putting them together
Section 4.1 was inducing Polarization via external electric fields
Section 4.2 was the electric field made from polarized objects
4.3 is now putting the two together.
The electric field then is due to the bound charges, and free charges (everything else)
This gives a definition of charge density as
put divergences together
New Gauss's law
as the electric displacement
Find The electric displacement for a wire (lambda) surrounded by a rubber insulator
this is inside the insulator.
outside the polarization goes away P =0
Similarities and differences
Gauss's law works for both E and D, just being mindful of the charge density.
But there is no kQ/r^2 for D. (no Coulombs law)
Another obvious difference is the curl.
but not necessarily for D
yet for electric displacement
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
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
"What does electric displacement actually tell us, as in, how is it useful to know the electric displacement. Is it just because it helps us to calculate other things?"
"Free charge? is it all of the available charge that is subject to polarization?"
"Could you explain how the boundary conditions are now different but similar to the old convention of the E fields? And maybe give a refresher on the E field boundary conditions?"