Lecture 5 Electric Flux Density and Dielectric Constant Boundary Conditions

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Lecture 5Electric Flux Density and Dielectric
ConstantBoundary Conditions
Electromagnetics Prof. Viviana Vladutescu
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Electric Flux Density
Gausss Law The total outward flux of the
dielectric displacement (or simply the outward
flux) over any closed surface is equal to the
total free charge enclosed in the surface
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Where- e is the absolute permittivity (F/m)
-er is the relative permittivity or the
dielectric constant of the medium
-e0 is the permittivity of free space
-?e is the electric susceptibility
(dimensionless)
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Material Dielectric Constants
Vacuum 1 Glass 5-10 Mica 3-6 Mylar 3.1
Neoprene 6.70 Plexiglas 3.40 Polyethylene 2.25
Polyvinyl chloride 3.18 Teflon 2.1
Germanium 16 Strontiun titanate 310 Titanium
dioxide (rutile) 173 perp 86 para Water 80.4
Glycerin 42.5 Liquid ammonia(-78C 25 Benzene
2.284 Air(1 atm) 1.00059 Air(100 atm) 1.0548
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Homogeneous -er independent of position Anisotrop
ic er is different for different of the
electric field
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Biaxial, Uniaxial and Isotropic Medium
-biaxial
-uniaxial
-isotropic
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KDP ADP crystals Electric field along optic
axis
Uniaxial crystal becomes biaxial with applied
field!
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GaAs CdTe crystals Electric field along optic
axis
Isotropic crystal become biaxial with applied
field!
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Dielectric Strength

• The maximum electric field intensity that a
  dielectric material can stand without breakdown

Material Dielectric Strength (V/m)
Air 3e6
Bakelite 24e6
Neoprene rubber 12e6
Nylon 14e6
Paper 16e6
Polystyrene 24e6
Pyrex glass 14e6
Quartz 8e6
Silicone oil 15e6
Strontium titanate 8e6
Teflon 60e6

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Boundary Conditions
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Medium 12 are dielectrics
CONDITION I (tangential components)
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Condition I (tangential components)
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CONDITION II (normal components)
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Condition II (normal components)
The normal component of D field is discontinuous
across an interface where a surface charge
exists, the amount of discontinuity being equal
to the surface charge density
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The magnitude of E2
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Boundary conditions at a Dielectric/Conductor
Interface
-inside a good conductor
E0 ET0 D0
Dn?s
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Practice Problems
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Divergence Theorem and Gausss Law
Suppose D 6rcosf af C/m2. (a) Determine the
charge density at the point (3m, 90?, -2m). Find
the total flux through the surface of a
quartered-cylinder defined by 0 r 4m, 0
f 90?, and -4m z 0 by evaluating (b) the
left side of the divergence theorem and (c) the
right side of the divergence theorem. (a)
(b)
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note that the top, bottom and outside integrals
yield zero since there is no component of D in
the these dS directions.
So,
(c)
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Electric Potential
The potential field in a material with er 10.2
is V 12 xy2 (V). Find E, P and D.
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Boundary Conditions
For z 0, er1 9.0 and for z gt 0, er2 4.0.
If E1 makes a 30? angle with a normal to the
surface, what angle does E2 make with a normal to
the surface?
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Therefore
also
and after routine math we find
Using this formula we obtain for this problem q2
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