ENGR-45_Lec-10_Dielectrics.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 45 Electrical Properties-3

ENGR-45_Lec-10_Dielectrics.ppt 2 Bruce Mayer, PE Engineering-45: Materials of Engineering 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

ENGR-45_Lec-10_Dielectrics.ppt 3 Bruce Mayer, PE Engineering-45: Materials of Engineering 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  The Quantity of the Separated Charge, Q, is Proportional to V  Look for Constant of Proportionality, C

ENGR-45_Lec-10_Dielectrics.ppt 4 Bruce Mayer, PE Engineering-45: Materials of Engineering 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 Where –Q  Charge (A-s or Coulombs) –V  Elect. Potential (V) –C  Capacitance (A-s/V or Coul/V or Faradays [Farads, F])

ENGR-45_Lec-10_Dielectrics.ppt 5 Bruce Mayer, PE Engineering-45: Materials of Engineering 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  Introducing a Constant of proportionality between C & A/ℓ

ENGR-45_Lec-10_Dielectrics.ppt 6 Bruce Mayer, PE Engineering-45: Materials of Engineering Electrical Capacitance cont.3  For a DiElectric Filled Cap Sometimes called “k”, the Dielectric Constant is ALWAYS Positive with a Magnitude greater than Unity Where –   Permittivity of the Dielectric Medium (F/m)  Using  0 as a BaseLine, Define a Material’s RELATIVE Dielectric Constant

ENGR-45_Lec-10_Dielectrics.ppt 7 Bruce Mayer, PE Engineering-45: Materials of Engineering Electrical 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”  Thus the Dielectric E-Field Strength

ENGR-45_Lec-10_Dielectrics.ppt 8 Bruce Mayer, PE Engineering-45: Materials of Engineering Examples  r = E bd = 3 x 10 6 V/m (  75 V/mil)  For Air at Room Conditions

ENGR-45_Lec-10_Dielectrics.ppt 9 Bruce Mayer, PE Engineering-45: Materials of Engineering 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 Magnetic DiPole –“North” and “South” “Poles” Separated  Note: These Entities ALWAYS exist in Tandem; There is NO Magnetic MonoPole

ENGR-45_Lec-10_Dielectrics.ppt 10 Bruce Mayer, PE Engineering-45: Materials of Engineering Field Vectors cont  Consider an Electric DiPole with Charge, q, and Separation, d  The DiPole Moment, p, is Quantified Magnitude = qd 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

ENGR-45_Lec-10_Dielectrics.ppt 11 Bruce Mayer, PE Engineering-45: Materials of Engineering Field 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

ENGR-45_Lec-10_Dielectrics.ppt 12 Bruce Mayer, PE Engineering-45: Materials of Engineering 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 = Q 0  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 Q 0 +Q’  The Dielectric Charges Nearest the Plates Orient Oppositely to the Added Plate Charge – See (c)

ENGR-45_Lec-10_Dielectrics.ppt 13 Bruce Mayer, PE Engineering-45: Materials of Engineering 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

ENGR-45_Lec-10_Dielectrics.ppt 14 Bruce Mayer, PE Engineering-45: Materials of Engineering Origins of DiElectric Const cont Capital-P Units Should be Coul/sq-m AND dipole-moments/cu-m  P vs p Units Analysis 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

ENGR-45_Lec-10_Dielectrics.ppt 15 Bruce Mayer, PE Engineering-45: Materials of Engineering Polarization 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

ENGR-45_Lec-10_Dielectrics.ppt 16 Bruce Mayer, PE Engineering-45: Materials of Engineering 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: Where –d i  Relative Displacement (m)  Total Polarization for any Material is the Sum of the Three Constituent Types

ENGR-45_Lec-10_Dielectrics.ppt 17 Bruce Mayer, PE Engineering-45: Materials of Engineering  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 At Frequencies, f r, That exceed 1/  r DiPoles CanNOT keep Up with the Applied Field; Reducing the Dielectric Effect

ENGR-45_Lec-10_Dielectrics.ppt 18 Bruce Mayer, PE Engineering-45: Materials of Engineering  r Comparison  Relaxation Frequency, f r, progression Fastest → Electronic Medium → Ionic Slowest → Orientation

ENGR-45_Lec-10_Dielectrics.ppt 19 Bruce Mayer, PE Engineering-45: Materials of Engineering All Done for Today Electrical Capacity

ENGR-45_Lec-10_Dielectrics.ppt 20 Bruce Mayer, PE Engineering-45: Materials of Engineering WhiteBoard Work  Let’s Work Prob 18.59W Given, Polarization P = Coul/sq-m Find  r for E = 50 kV/m Calculate the Electric Charge Displacement, D