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Bruce Mayer, PE Registered Electrical & Mechanical Engineer [email protected]

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Engineering 45

ElectricalProperties-3

Bruce Mayer, PE

Registered Electrical & Mechanical [email protected]

- 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

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

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])

Introducing a Constant of proportionalitybetween C & A/ℓ

- 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

For a DiElectric Filled Cap

- Where
- Permittivity of the Dielectric Medium (F/m)

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

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

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

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

- “North” and “South” “Poles” Separated

Consider an Electric DiPole with Charge, q, and Separation, d

- Direction Neg→Pos

- The Torque Can Be applied with an Electric Field

Not Aligned →Torque

Aligned →NO Torque

- The DiPole Moment, p, is Quantified
- Magnitude = q•d

- The Process of Pole Alignment is called“polarization”

Consider again the ||-Plate Cap

The Areal Density of Charges on Each Plate, D

- 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)

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)

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

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

- P vs p Units Analysis

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

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

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:

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

- Where
- di Relative Displacement (m)

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

- Relaxation Frequency, fr, progression
- Fastest → Electronic
- Medium → Ionic
- Slowest → Orientation

ElectricalCapacity

- 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