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lorentz model , its application, Lecture notes of Electrodynamics

Western Illinois University (WIU)Electrodynamics
Prof. Chang Gulla

classicL THEORY OF LORENTZ MODEL, comparison with drudge model, use in superconductor

Typology: Lecture notes

2020/2021

Uploaded on 02/25/2021

Rista007
Rista007 🇺🇸

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6/3/2020
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AdvancedElectromagnetics:
21st CenturyElectromagnetics
LorentzOscillatorModel
LectureOutline
•Highlevelpictureofdielectricresponse
•Qualitativedescriptionofresonance
•DerivationofLorentzoscillatormodel
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Download lorentz model , its application and more Lecture notes Electrodynamics in PDF only on Docsity!

  • • • HighQualitativeDerivation levelLorentz picture ofdescription^21 Lorentz^ Advancedst^ Lecture^ Century of^ Oscillator dielectric oscillator ofElectromagnetics:^ Electromagnetics resonance^ Outline response model^ Model 2
  • Moving High Level Pictureof Dielectric ChargesResponse Radiate Waves (1 of 2) Slide
    • This is called the single‐charge radiation model (Heaviside,outward travelling wave 1894).
    • Moving Charges Dielectric Radiate Slab Waves (2 of 2)
  • It is desired to understand why a dielectric exhibits an electromagnetic response.
  • Without and at rest. an applied electric field 𝐸 Atoms Applied, the electron at Wave“clouds” Rest around the nuclei are symmetric
  • The producing electric “clouds” field 𝐸 ofthat a electromagnetic are offset. wave pushes the electrons away from the nuclei
  • The produce motion an overallof the charges slowing emits effect Secondary secondary on the wave. waves Wavesthat interfere with the applied wave to
    • Description ofResonance Qualitative Slide
  • Visualizing Visualizing Resonance Resonance • • • Driving amplitudeDisplacement drivingThere – Low – on exists forceforce Resonance a Frequencyis isDC able in offset phase to modulate with
    • • • Driving displacementsDisplacement with push displacement) thecorrespond force driving can is 90° outforce causeto nulls (i.e. large of of peaksphase of
  • Visualizing Response Resonance of A Harmonic • • Displacement amplitudeDisplacement with perfectly – High driving oppose Oscillator force Frequency hasis 180° out it. invanishing order of to phase
    • Amplitude0°> 0  res>> 90°^0 180° 0 Phase Lag
  • Amplitude Impulse Excitation Time, BallResponse t DampingDisplacement loss of a Harmonic Oscillator
    • Lorentz Oscillator Derivation ofModel Slide
    • dampermassMass on Lorentz a Spring Equationspring Oscillator of MotionAtomic Model Model electronnucleus Electricfield cloud 𝐸 ൅െ
  • acceleration m  m e mass electron force of m an ^2 t^2 r   m frictional   damping (loss/sec)  force rt  rate  m  restoring^020  r  K m   forcenaturalfrequency qE  electric force
  • Fourier  m   m  mj    Charge 2 Transform 2  r  2 t  r 2   j   mmm  Displacement     jr the t   m  FourierSimplify r   m  0 2 Equation  transform  r  0 2 m  r   0 2   r  𝑟⃗ 𝜔   qE of   qE Motion qE   
    • r  r      m  ^2   j  m m   q The chargee m  displacement Solve for^0 0 2 2 is r displaced  E   r     ^2   𝑟⃗ 𝜔 qE from  j  describes its equilibrium how far position.
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  •   ForThis  𝛼 𝜔 Definition simplicity, is  the is a Lorentz tensor mq the of**^2 e scalarquantitypolarizability for SorryLorentz form 0 2 for for  thewill anisotropic  confusingbePolarizability: a^1 adoptedsingle 2  materials. atom.notation, j here. but   here  The measure are displaced is NOT displaced. Lorentz absorption. of in  how polarizabilitysome Charge easily directions  mayelectrical E  𝛼 𝜔 be  that more  charges isothers. a easily
    • There is Electric Susceptibility Definition:some N Unpolarized Polarization randomness Number of atoms per unit volume PP to  the   polarized  N Polarized V^1 Per  atoms V  with   i so someUnit a AppliedE statistical ‐Field Nq randomness m e 2 VolumeAverageAll approach 0 2 𝜒 billions Statistical volume averageୣ E    dipole 2  𝜔 isand  taken j Equivalent  trillionsmoment to(1 of 2)𝑃 𝜔 compute of uniformover them!!! AppliedEall the‐ polarizationField atoms average. in a material.
  • A toThis material leads tobecomes P  an e    expression    polarized  N 0  e   0 for  𝑃 the E in measure polarize e ( electricthe   ) Nq  is 0 presence m called a 2 ofe material. susceptibility:how  the 0 2 easily  electric of  an 1 2 an electric susceptibility electric j  fieldfield 𝐸 and𝐸 can according is a
  • The electric • • • • NoteTheRealElectric location materials Electric Susceptibilitythis susceptibility Plotsusceptibilityis the e of  have atomssusceptibility of many isis the importantElectric sources 0 2 transfer ofof aa m  dielectric of q dielectric because 0 e 2 function p  2 resonance 1.602176468.85418781769.10938188 j Susceptibility whichthey of the and materialcan has oscillator all 10 influence 10 only of  10 ^1931 𝜒these  one Ckg 12 ୣ is:system. F m eachresonance.p 2 must𝜔 other. be Nq 0 𝜒added m (2 of 2) This 2 ୣ e plasma frequency together.was𝜔 ignored.
    •  e e ^0 0   e  0 p^0 ^2   ^0 2   ^2 p^2  j e  ^0    ^0 p^2  ^0  e  ^0 ^90 Γ is FWHM for 𝜒௘ 𝜔 e   ଶ e.   ^180 ^0 Slide