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

1. Engineering 45 ElectricalProperties-3 Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. 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

3. 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

4. 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])

5. 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

6. 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

7. 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”

8. Examples • r = 1.00059 • Ebd= 3 x 106 V/m (75 V/mil) • For Air at RoomConditions

9. 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

10. 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”

11. 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)

12. 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)

13. 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.

14. 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

15. Electronic 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

16. Ionic 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)

17. 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

18. r Comparison • Relaxation Frequency, fr, progression • Fastest → Electronic • Medium → Ionic • Slowest → Orientation

19. All Done for Today ElectricalCapacity

20. 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