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# Fields and Waves

Fields and Waves. Lesson 3.1. ELECTROSTATICS - INTRODUCTION. ELECTRICAL CHARGES. SOURCE of Electrostatic E-Field is CHARGE. Examples of various charge distributions:. 1. Point charge - Q (units of Coulomb).

## Fields and Waves

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### Presentation Transcript

1. Fields and Waves Lesson 3.1 ELECTROSTATICS - INTRODUCTION Darryl Michael/GE CRD

2. ELECTRICAL CHARGES SOURCE of Electrostatic E-Field is CHARGE Examples of various charge distributions: 1. Point charge - Q (units of Coulomb) - model individual particle (eg. Electron) or a well-localized group of charge particles 2. Volume Charge Density - ror rv (units of Coulomb/m3) - large # of particles - ignore discrete nature to smooth out distribution Eg. Doped Region of Semiconductor, e-beam in a cathode ray tube ( Beam has finite radius )

3. ELECTRICAL CHARGES Other examples of Charge Distribution…….. 3. Surface Charge Density - ror rs (units of Coulomb/m2) Eg. Very thin charge layer on conductor surface 4. Line Charge Density - ror rl (units of Coulomb/m) - not as physically realizable Eg. Model for a wire, electron beam from far

4. ELECTRICAL CHARGES Maxwell’s equation: More generally, Derived from: or Do Problem 1

5. COULOMB’S LAW (force), between point charges Q1 Unit vector in r-direction Force on Charge 2 by Charge 1 R Q2

6. COULOMB’S LAW - E Field ,of Q1 is Unit vector pointing away from Q1 Then, - we work with E-Field because Maxwell’s equations written in those terms

7. Point charge E-FIELDS , is a VECTOR Field How do we represent it? - Field points in the direction that a +ve test charge would move Represent using Arrows : Direction and Length Proportional to Magnitude or strength of E-Field

8. +Q y x -Q E-FIELDS Computation of E-fields from multiple charges: Example: DIPOLE - 2 separated opposite polarity point charges Apply superposition of Fields Planes of symmetry: Horizontal axis: Ex cancels, Ey adds +Q vector Vertical axis: only Ey component -Q Resulting vector

9. E-FIELDS - Some examples

10. E-FIELDS - Some examples

11. E-FIELDS - Dipole

12. E-FIELDS How would the DIPOLE field lines change if the charges were the same polarity? APPLICATION of SUPERPOSITION • Usually text has many examples of setting up this integral • In the course we will do some discrete Scases Do Problem 2

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