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Engineering 45
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Engineering 45. Electrical Properties-3. Bruce Mayer, PE Registered Electrical & Mechanical Engineer Learning Goals – Dielectrics. Understand the fundamentals of Electrical Capacitance How Certain Materials can Dramatically Increase the Electrical Capacity

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Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege

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Bruce mayer pe registered electrical mechanical engineer bmayer chabotcollege

Engineering 45


Bruce Mayer, PE

Registered Electrical & Mechanical

Learning goals dielectrics

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

Electrical 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

Electrical Capacitance

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

  • Look for Constant of Proportionality, C

Electrical capacitance cont

The Value of C can Found from an Expression that is Analogous to Ohm’s Eqn

Electrical Capacitance cont.

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

  • Where

    • Q  Charge (A-s or Coulombs)

    • V  Elect. Potential (V)

    • C  Capacitance (A-s/V or Coul/V or Faradays [Farads, F])

Electrical capacitance cont 2

Introducing a Constant of proportionalitybetween C & A/ℓ

Electrical Capacitance cont.2

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

  • Where

    • A  Plate Area (sq-m)

    • l  Plate Distance (m)

    • 0  Permittivity of Free Space (vacuum) = 8.85x10−12 F/m

Electrical capacitance cont 3

For a DiElectric Filled Cap

Electrical Capacitance cont.3

  • Where

    •   Permittivity of the Dielectric Medium (F/m)

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

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

    Electrical terms

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

    Electrical Terms

    and Current will Flow

    • Thus the Dielectric E-Field Strength

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



    • r = 1.00059

    • Ebd= 3 x 106 V/m (75 V/mil)

    • For Air at RoomConditions

    Electric 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

    Electric DiPole

    • Magnetic DiPole

      • “North” and “South” “Poles” Separated

        • Note: These Entities ALWAYS exist in Tandem; There is NO Magnetic MonoPole

    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

  • Field Vectors cont

    Not Aligned →Torque

    Aligned →NO Torque

    • The DiPole Moment, p, is Quantified

      • Magnitude = q•d

    • The Process of Pole Alignment is called“polarization”

    Field vectors cont 2

    Consider again the ||-Plate Cap

    The Areal Density of Charges on Each Plate, D

    Field Vectors cont.2

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

    • Where

      •  & E from Before

      • D  Charge Density (Coul/sq-m)

    Origins of dielectric constant

    Consider Two Caps: One in a Vacuum, and one with a Dielectric Material Between the Plates

    Origins of DiElectric Constant

    • 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

    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

    Origins of DiElectric Const cont.

    Origins of dielectric const cont1

    Origins of DiElectric Const cont

    • Where

      • P  is the DiElectric POLARIZATIONcharge, (Coul/sq-m)

  • In Concept, P → TOTAL DiPole Moment Per Unit-Volume for the Dielectric Material

  • For Many DiElectrics

    • P vs p Units Analysis

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

    Polarization types


    Polarization Types

    • 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

    Polarization types cont


    Polarization Types cont.

    • 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:

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

    • Where

      • di Relative Displacement (m)

    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

     Frequency Dependence

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

    R comparison

    r Comparison

    • Relaxation Frequency, fr, progression

      • Fastest → Electronic

      • Medium → Ionic

      • Slowest → Orientation

    All done for today

    All Done for Today


    Whiteboard work

    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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