[email protected] engr-45_lec-10_dielectrics.ppt 1 bruce mayer, pe engineering-45: materials...

[email protected] • ENGR-45_Lec-10_Dielectrics.ppt1

Bruce Mayer, PE Engineering-45: Materials of Engineering

Bruce Mayer, PERegistered Electrical & Mechanical Engineer

[email protected]

Engineering 45

ElectricalElectricalPropertiesProperties

-3-3



Learning Goals – DielectricsLearning 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



Electrical CapacitanceElectrical Capacitance Consider Two

Conductive Plates Separated by a Small & Empty Gap With a Voltage Applied (right)

Since No Current Can Flow Across The Gap• Positive Charges

Accumulate on Top

• Negative Charges Accumulate on Bot

The Quantity of the Separated Charge, Q, is Proportional to V

VQ Look for Constant of

Proportionality, C



Electrical Capacitance cont.Electrical Capacitance cont. The Value of C can

Found from an Expression that is Analogous to Ohm’s Eqn

• For || plates in a Vacuum C is proportional to the Plate AREA, and the inverse Separation LENGTH

CVQ • Where

– Q Charge (A-s or Coulombs)

– V Elect. Potential (V)– C Capacitance

(A-s/V or Coul/V or Faradays [Farads, F])

l

AC



Electrical Capacitance cont.2Electrical Capacitance cont.2

• Filling The Gap with a NONconductive Material INCREASES the Charge Accumulation Thru the DiElectric Effect

l

Aε C 0

• Where– A Plate Area (sq-m)– l Plate Distance (m) 0 Permittivity of

Free Space (vacuum) = 8.85x10−12 F/m

Introducing a Constant of proportionalitybetween C & A/ℓ



Electrical Capacitance cont.3Electrical Capacitance cont.3 For a DiElectric

Filled Cap

• Sometimes called “k”, the Dielectric Constant is ALWAYS Positive with a Magnitude greater than Unity

l

Aε C

• Where Permittivity of the

Dielectric Medium (F/m)

Using 0 as a BaseLine, Define a Material’s RELATIVE Dielectric Constant

0εε r



Electrical TermsElectrical Terms Electric Field is the

ratio of a Voltage Drop to Distance over Which the Drop Occurs; to whit

and Current will Flow

Now as V Increases toward at Some Point the Dielectric will “Break Down”

mV

lVΕ

/units

mV

lVΕ flowibd

/units

Thus the Dielectric E-Field Strength



ExamplesExamples

r = 1.00059

• Ebd = 3 x 106 V/m (75 V/mil)

For Air at RoomConditions



Electric DiPoleElectric DiPole What is a “DiPole”?

• DiPole Refers to the Physical SEPARATION of TWO, OPPOSITE-polarity, and thus Attractive, “Charge Entities”

Two Classical Types• Electric DiPole

– “+” & “-” Charges Separated

• Magnetic DiPole– “North” and “South”

“Poles” Separated Note: These Entities

ALWAYS exist in Tandem; There is NO Magnetic MonoPole



Field Vectors contField Vectors cont Consider an Electric

DiPole with Charge, q, and Separation, d

The DiPole Moment, p, is Quantified• Magnitude = q•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 Process of Pole Alignment is called“polarization”

Not Aligned

→Torque Aligned →NO Torque



Field Vectors cont.2Field Vectors cont.2 Consider again the

||-Plate Cap The Areal Density of

Charges on Each Plate, D

• Where & E from Before– D Charge Density

(Coul/sq-m)

• Since a Cap Configuration “Displaces” Charges from one Plate to Another, The Quantity D is also Called the DIELECTRIC (charge) DISPLACEMENT

DEl

VV

lD

A

Q

Vl

ACVQ



Origins of DiElectric ConstantOrigins 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)



Origins of DiElectric Const cont.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

PED 0



Origins of DiElectric Const contOrigins of DiElectric Const cont

• Capital-P Units Should be Coul/sq-m AND dipole-moments/cu-m

PED 0

EP r 10

P vs p Units Analysis

33

22

m

p

m

mCoulP

m

m

m

Coul

m

CoulP

mCouldqp

• 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



Polarization TypesPolarization Types Electronic

Orientation • Occurs Only in Materials

that have PERMANENT Dipole Moments (atomic or molecular)

• The Field Polarizes the Originally Randomly oriented Dipoles

• The Applied Field Displaces the e- “cloud” relative to the Nucleus, resulting in noncoincident charge centers– Occurs to some Extent

in all Atoms



Polarization Types cont.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:

ii dqp • Where

– di Relative Displacement (m)

Total Polarization for any Material is the Sum of the Three Constituent Types

oietot PPPP



Frequency DependenceFrequency 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

• At Frequencies, fr, That exceed 1/r DiPoles CanNOT keep Up with the Applied Field; Reducing the Dielectric Effect



rr Comparison Comparison Relaxation Frequency, fr,

progression• Fastest → Electronic• Medium → Ionic• Slowest → Orientation



All Done for TodayAll Done for Today

ElectricalCapacity



WhiteBoard WorkWhiteBoard 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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