Transcript ENGR-45_Lec-10_DiElectrics

Engineering 45
Electrical
Properties-3
Bruce Mayer, PE
Registered Electrical & Mechanical Engineer
[email protected]
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-10_Dielectrics.ppt
Learning Goals – Dielectrics
 Understand the fundamentals of
Electrical Capacitance
 How Certain Materials can Dramatically
Increase the Electrical Capacity
 Understand Dipoles and Polarization
 Learn the Types of Polarization
 Dielectric-Constant vs Frequency
Behavior
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
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Electrical Capacitance
 Consider Two
Conductive Plates
Separated by a
Small & Empty Gap
With a Voltage
Applied (right)
 The Quantity of the
 Since No Current Can Separated Charge, Q,
Flow Across The Gap
is Proportional to V
• Positive Charges
Accumulate on Top
• Negative Charges
Accumulate on Bot
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QV
 Look for Constant of
Proportionality, C
Bruce Mayer, PE
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Electrical Capacitance cont.
 The Value of C can
Found from an
Expression that is
Analogous to Ohm’s
Eqn
Q  CV
• Where
– Q  Charge (A-s or
Coulombs)
– V  Elect. Potential (V)
– C  Capacitance
(A-s/V or Coul/V or
Faradays [Farads, F])
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• For || plates in a
Vacuum C is
proportional to the Plate
AREA, and the inverse
Separation LENGTH
A
C
l
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Electrical Capacitance cont.2
 Introducing a
Constant of
proportionality
between C & A/ℓ
A
C  ε0
l
• Where
– A  Plate Area (sq-m)
– l  Plate Distance (m)
– 0  Permittivity of Free
Space (vacuum) =
8.85x10−12 F/m
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• Filling The Gap with a
NONconductive
Material INCREASES
the Charge
Accumulation Thru the
DiElectric Effect
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Electrical Capacitance cont.3
 For a DiElectric
Filled Cap
•
A
Cε
l
Where
–   Permittivity of the
Dielectric Medium
(F/m)
 Using 0 as a
BaseLine, Define a
Material’s RELATIVE
Dielectric Constant
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 r  ε ε0  
• Sometimes called “k”,
the Dielectric Constant
is ALWAYS Positive
with a Magnitude
greater than Unity
Bruce Mayer, PE
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Electrical Terms
 Electric Field is the
ratio of a Voltage
Drop to Distance
over Which the Drop
Occurs; to whit
Ε  V l
units  V / m
 Now as V Increases
toward  at Some
Point the Dielectric
will “Break Down”
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and Current will Flow
 Thus the Dielectric
E-Field Strength
Εbd  Vi  flow l
units  V / m
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Examples
 For Air at Room • r = 1.00059
6 V/m (75 V/mil)
•
E
=
3
x
10
bd
Conditions
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Bruce Mayer, PE
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Electric DiPole
 What is a “DiPole”?
• DiPole Refers to the
Physical
SEPARATION of
TWO, OPPOSITEpolarity, and thus
Attractive, “Charge
Entities”
 Two Classical Types
• Electric DiPole
• Magnetic DiPole
– “North” and “South”
“Poles” Separated
 Note: These Entities
ALWAYS exist in
Tandem; There is NO
Magnetic MonoPole
– “+” & “-” Charges
Separated
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Bruce Mayer, PE
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Field Vectors cont
 Consider an Electric
DiPole with Charge,
q, and Separation, d
• Direction 
Neg→Pos
 We call this a
“Moment” because of
the the DiPole can be
Twisted
• The Torque Can Be
applied with an
Electric Field
 The DiPole Moment,
p, is Quantified
• Magnitude = q•d
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Not
Aligned
→Torque
Aligned →NO
Torque
• The Process of Pole
Alignment is called
“polarization”
Bruce Mayer, PE
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Field Vectors cont.2
 Consider again the
||-Plate Cap
 The Areal Density of
Charges on Each
Plate, D
Q  CV 
A
V
• Since a Cap Configuration
l
“Displaces” Charges from
Q

V
one Plate to Another, The
 D  V   E  D
A
l
l
Quantity D is also Called
• Where
the DIELECTRIC (charge)
–  & E from Before
DISPLACEMENT
– D  Charge Density
(Coul/sq-m)
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
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Origins of DiElectric Constant
 Consider Two Caps: One in a
Vacuum, and one with a Dielectric
Material Between the Plates
 Charge on the Vacuum Plates = Q0
 Then The Dielectric Slides
Between the Plates and
DiPoles Align to the E-Field
• i.e. The DiElectric Becomes Electrically
POLARIZED – See (b)
 Adding the DiElectric Increases the
Plate Charge to Q0+Q’
 The Dielectric Charges Nearest the
Plates Orient Oppositely to the
Added Plate Charge – See (c)
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Bruce Mayer, PE
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Origins of DiElectric Const cont.
• Note that Regions Removed from the
Dielectric Surface Do Not Contribute to
the ElectroStatic Balance, and thus this
region is Electrically NEUTRAL
 The Dielectric Surface Charge Tends
to Cancel the Vacuum Charge
• Hence the Battery Must Supply added
Charge to Bring the interface Regions to
Electrical Neutrality
– This Occurs withOUT an increase in V;
and to the Q/V quotient (C) increases
 Quantify the Increase in D as
D  0  E  P
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-10_Dielectrics.ppt
Origins of DiElectric Const cont
D  0  E  P
• Where
– P  is the DiElectric POLARIZATION
charge, (Coul/sq-m)
 In Concept, P → TOTAL DiPole
Moment Per Unit-Volume for the
Dielectric Material
 For Many DiElectrics
P   0  r  1E
• Capital-P Units Should be Coul/sq-m
AND dipole-moments/cu-m
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 P vs p Units
Analysis
p  q  d  Coul  m
Coul Coul m
P 2  2
m
m m
Coul  m
p
P

m3
m3
Bruce Mayer, PE
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Polarization Types
 Electronic
• The Applied Field
Displaces the e- “cloud”
relative to the Nucleus,
resulting in noncoincident
charge centers
– Occurs to some Extent
in all Atoms
 Orientation
• Occurs Only in Materials
that have PERMANENT
Dipole Moments (atomic
or molecular)
• The Field Polarizes the
Originally Randomly
oriented Dipoles
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Polarization Types cont.
 Ionic
• The Applied Field
Causes Relative
Displacement of the
Anion and Cation Charge
Centers Which Causes a
Net Dipole Moment
• The Magnitude of The
Dipole Moment for each
ion pair:
pi  q  di
• Where
– di  Relative
Displacement (m)
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 Total Polarization for any
Material is the Sum of
the Three Constituent
Types
Ptot  Pe  Pi  Po
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 Frequency Dependence
 AC Electric signals
Are often Applied at
High Frequencies to
Capacitive Materials
 Since Dipole
Alignment MUST
have some FINITE
Relaxation Time, r,
Expect some
Dielectric Frequency
Dependence
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• At Frequencies, fr,
That exceed 1/r
DiPoles CanNOT
keep Up with the
Applied Field;
Reducing the
Dielectric Effect
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r Comparison
 Relaxation Frequency, fr,
progression
• Fastest → Electronic
• Medium → Ionic
• Slowest → Orientation
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-10_Dielectrics.ppt
All Done for Today
Electrical
Capacity
Engineering-45: Materials of Engineering
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Bruce Mayer, PE
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WhiteBoard Work
 Let’s Work Prob 18.59W
• Given, Polarization P =
10-6 Coul/sq-m
• Find r for E = 50 kV/m
• Calculate the Electric
Charge Displacement, D
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Bruce Mayer, PE
[email protected] • ENGR-45_Lec-10_Dielectrics.ppt