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NASSP Self-study Review 0f Electrodynamics Created by Dr G B Tupper

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Presentation on theme: "NASSP Self-study Review 0f Electrodynamics Created by Dr G B Tupper"— Presentation transcript:

1 NASSP Self-study Review 0f Electrodynamics Created by Dr G B Tupper

2 The following is intended to provide a review of classical electrodynamics at the 2 nd and 3 rd year physics level, i.e. up to chapter 9 of Griffiths book, preparatory to Honours. You will notice break points with questions. Try your best to answer them before proceeding on – it is an important part of the process!

3 Basics Maxwells equations: Lorentz force:

4 Basics Mathematical tools: – Gauss Theorem – Stokes Theorem – Gradient Theorem – Greens function

5 Basics Mathematical tools: – Second derivatives – Product rules Potentials

6 Questions Where is charge conservation? Where is Coulombs law? Where is Biot-Savart law? What about Ohms law? Where is charge conservation? Where is Coulombs law? Where is Biot-Savart law? What about Ohms law?

7 Work done on charge Power (Lorentz) Now So Use Ampere-Maxwell

8 Conservation of energy Identity Use Faraday So

9 Poyntings Theorem Define – Mechanical energy density – Electromagnetic energy density – Poynting vector EM fields carry energy

10 Questions Problem: an infinite line charge along z-axis moves with velocity : Determine

11 Waves in vacuum Maxwells equations: Curl of Faraday:

12 Waves in vacuum Use Gauss & Ampere-Maxwell; wave equation Speed of light Monochromatic plane-wave solutions constant Transverse

13 Questions What is the meaning of the wave-number ? What is the meaning of angular frequency ? What is the associated magnetic field? Wavelength Period

14 Monochromatic plane-wave

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17 Energy density Poynting vector Momentum density

18 Monochromatic plane-wave Time average Intensity

19 Questions A monochromatic plane-polarized wave propagating in the z-direction has Cartesian components in phase :. In contrast, a circularly-polarized wave propagating in the z-direction has Cartesian components out of phase: Describe in words what such a circularly-polarized wave looks like. One of the two casess left-handed, and the other is right handed – which is which? i Determine the corresponding magnetic field. Determine the instantaneous energy-density and Poynting vector.

20 Electrostatics in matter Electric field polarizes matter – Potential in dipole approximation – Bound charge density Polarization: dipole moment per unit volume Polarization: dipole moment per unit volume

21 Electrostatics in matter Rewrite Gauss law – Displacement field – For linear isotropic media Free charge density

22 Dielectric constant

23 Magnetostatics in matter Magnetic field magnetizes matter – Vector potential Magnetization: magnetic moment per unit volume Magnetization: magnetic moment per unit volume

24 Magnetostatics in matter; Dipole moment proof Picture Dipole approximation For arbitrary constant vector Therefore =0 Q.E.D.

25 Magnetostatics in matter – Bound current density Rewrite Amperes law – Induction – For linear isotropic media Free current density

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27 Electrodynamics in matter New feature Rewrite Ampere-Maxwell

28 Electrodynamics in matter Maxwells equations Constitutive relations Linear isotropic media

29 Electrodynamics in matter Boundary conditions

30 Electrodynamics in matter Energy density Poynting vector

31 Electromagnetic waves in matter Assume electrical neutrality In general there may be mobile charges; use – Resistivity Conductivity

32 Electromagnetic waves in matter Maxwells equations – Curl of Faraday – For constant use Ampere-Maxwell

33 Electromagnetic waves in matter Wave equation In an ideal insulator – Phase velocity – Plane wave solution New Index of refraction

34 Questions 1.What do you expect happens in real matter where the conductivity doesnt vanish? 2.Which is more basic: wavelength or frequency?

35 Electromagnetic waves in matter Take propagation along z-axis – Complex ansatz – Substitution gives – Solution

36 Electromagnetic waves in matter Thus general solution is Transverse Phase Attenuation! Frequency dependant: dispersion

37 Electromagnetic waves in matter Limiting cases – High frequency – Low frequency Good insulator Good conductor Note: at very high frequencies conductivity is frequency dependant

38 Electromagnetic waves in matter Magnetic field – take for simplicity

39 Electromagnetic waves in matter Good conductor

40 Questions What one calls a good conductor or good insulator is actually frequency dependant; i.e. is or ? Find the value of for pure water and for copper metal. Where does it lie in the electromagnetic spectrum in each case? For each determine the high-frequency skin depth. For each determine the skin depth of infrared radiation ( ). In the case of copper, what is the phase velocity of infrared radiation? In the case of copper, what is the ratio for infrared radiation?

41 Frequency dependence Electric field polarizes matter Model Restoring force Driving force Damping (radiation) …dynamically

42 Frequency dependence Electromagnetic wave – Rewrite in complex form – Steady state solution Natural frequency

43 Frequency dependence – Substitution of steady state solution – Dipole moment

44 Frequency dependence Polarization Complex permittivity Number of atoms/molecules per unit volume

45 Frequency dependence Even for a good insulator Low density (gases) Ignore paramagnetism/diamagnetism Absorption coefficient

46 Frequency dependence Low density Frequency dependent: dispersion

47 Frequency dependence Anomalous dispersion

48 Questions

49 Electromagnetic waves in Plasma Electrons free to move; inertia keeps positive ions almost stationary Model – Solution Electron mass No restoring force!

50 Electromagnetic waves in Plasma Current density Conductivity Electron number density Drude model

51 Electromagnetic waves in Plasma Electron collisions rare, so dissipation small Recall for conductor Purely imaginary!!

52 Electromagnetic waves in Plasma As – Above the plasma frequency: waves propagate with negligible loss – Below the plasma frequency: no propagation, only exponential damping Dispersion relationPlasma frequency F&F 2013 L46

53 Plasma - Ionosphere


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