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

SOURCE of Electrostatic E-Field is CHARGE 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 - r or 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 )

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

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

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

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

Proportional to Magnitude or strength of E-Field 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 Point charge Proportional to Magnitude or strength of E-Field

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

E-FIELDS - Some examples

E-FIELDS - Some examples

E-FIELDS - Dipole

APPLICATION of SUPERPOSITION 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 S cases Do Problem 2