Fields and Waves

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Fields and Waves
Lesson 3.4
ELECTROSTATICS - MATERIALS
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CONDUCTORS and DIELECTRICS
Conductors
Dielectrics
High conductivities s (for Copper) 5.8x107 S/m
Low conductivities s (for Rubber) 1x10-15 S/m
or 1/W-m
Semiconductors (mid ss)
Permittivities, e 1-100e0
Note e0 is the permittivity of free space/vacuum
8.854 x 10-12 F/m
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CONDUCTORS
Most electrons are stuck to the nucleus
But, 1 or 2 electrons per atom are free to move
This means that if you apply an external E-field,
the free electrons will move
Lattice of Nuclei
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CONDUCTORS
conductor
electrons
Apply external E-field,

• Force on electrons causes free electrons to move
• Charge displacement causes response E-field
  (opposite to applied external E-field)

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CONDUCTORS
The electrons keep moving until,
This means that
Do problem 1
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DIELECTRICS
electron cloud
nucleus
electron cloud centered on nucleus
Cloud shifts to setup
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DIELECTRICS
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DIELECTRICS
subtracts out bound charge
Define
Displacement Flux Density ( C/m2 )
Electric Field (V/m)
is due to bound/dielectric charge and free charge
is due to bound/dielectric charge only and
opposite sign
is due to free charge only
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FREE CHARGES
Examples of free charges
rs on conductor
electron beam
doped region of semi-conductor
Gauss Law uses just free charge
Most general form
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DIELECTRICS
Do Problem 2
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DIELECTRIC BREAKDOWN - part d of problem
Example Arc in Air
If E-field is too large, it will pull electrons
off from atom
These electrons are accelerated by the E-field
These accelerated electrons then collide with
more atoms that knock off more electrons
This is an AVALANCHE PROCESS
BREAKDOWN OCCURS if
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BOUNDARY CONDITIONS - Normal Components

• all derived from Maxwells equations

NORMAL COMPONENT
Take h ltlt a (a thin disc)
a
Material 1
TOP
h
Material 2
BOTTOM
Gaussian Surface
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BOUNDARY CONDITIONS - Normal Components
Case 1
REGION 2 is a CONDUCTOR, D2 E2 0
Case 2
REGIONS 1 2 are DIELECTRICS with rs 0
Can only really get rs with conductors
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BOUNDARY CONDITIONS - Tangential Components
w
Material 1
h ltlt w
h
Material 2
If region 2 is a conductor E1t 0
Note
Outside conductor E and D are normal to the
surface