NASSP Electrodynamics Review Self-study

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NASSP Self-studyReview 0f Electrodynamics
Created by Dr G B Tupper gary.tupper_at_uct.ac.za
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The following is intended to provide a review of
classical electrodynamics at the 2nd and 3rd 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!
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Basics

• Maxwells equations
• Lorentz force

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Basics

• Mathematical tools
• Gauss Theorem
• Stokes Theorem
• Gradient Theorem
• Greens function

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Basics

• Mathematical tools
• Second derivatives
• Product rules
• Potentials

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Questions

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

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Work done on charge

• Power (Lorentz)
• Now
• So
• Use Ampere-Maxwell

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Conservation of energy

• Identity
• Use Faraday
• So

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Poyntings Theorem

• Define
• Mechanical energy density
• Electromagnetic energy density
• Poynting vector
• EM fields carry energy

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Questions

• Problem an infinite line charge along z-axis
  moves with velocity
• Determine

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Waves in vacuum

• Maxwells equations
• Curl of Faraday

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Waves in vacuum

• Use Gauss Ampere-Maxwell wave equation
• Speed of light
• Monochromatic plane-wave solutions

constant
Transverse
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Questions

• What is the meaning of the wave-number ?
• What is the meaning of angular frequency ?
• What is the associated magnetic field?

Wavelength
Period
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Monochromatic plane-wave
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Monochromatic plane-wave

• Energy density
• Poynting vector
• Momentum density

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Monochromatic plane-wave

• Time average
• Intensity

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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.
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Electrostatics in matter

• Electric field polarizes matter
• Potential in dipole approximation
• Bound charge density

Polarization dipole moment per unit volume
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Electrostatics in matter

• Rewrite Gauss law
• Displacement field
• For linear isotropic media

Free charge density
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Dielectric constant
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• Magnetic field magnetizes matter
• Vector potential

Magnetization magnetic moment per unit volume
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• Picture
• Dipole approximation
• For arbitrary constant vector
• Therefore

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Q.E.D.
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• Bound current density
• Rewrite Amperes law
• Induction
• For linear isotropic media

Free current density
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• New feature
• Rewrite Ampere-Maxwell

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• Maxwells equations
• Constitutive relations
• Linear isotropic media

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• Boundary conditions

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• Energy density
• Poynting vector

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• Assume electrical neutrality
• In general there may be mobile charges use
• Resistivity

Conductivity
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• Maxwells equations
• Curl of Faraday
• For constant use Ampere-Maxwell

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• Wave equation
• In an ideal insulator
• Phase velocity
• Plane wave solution

New
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Questions

• What do you expect happens in real matter where
  the conductivity doesnt vanish?
• Which is more basic wavelength or frequency?

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• Take propagation along z-axis
• Complex ansatz
• Substitution gives
• Solution

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• Thus general solution is

Transverse
Phase
Attenuation!
Frequency dependant dispersion
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• Limiting cases
• High frequency
• Low frequency

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• Magnetic field take for simplicity

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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?    
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• Electric field polarizes matter
• Model

Restoring force
Driving force
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• Electromagnetic wave
• Rewrite in complex form
• Steady state solution

Natural frequency
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• Substitution of steady state solution
• Dipole moment

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• Polarization
• Complex permittivity

Number of atoms/molecules per unit volume
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• Even for a good insulator
• Low density (gases)

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• Low density

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Anomalous dispersion
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Questions
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• Electrons free to move inertia keeps positive
  ions almost stationary
• Model
• Solution

Electron mass
No restoring force!
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• Current density
• Conductivity

Drude model
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• Electron collisions rare, so dissipation small
• Recall for conductor

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• As
• Above the plasma frequency waves propagate with
  negligible loss
• Below the plasma frequency no propagation, only
  exponential damping

Dispersion relation
Plasma frequency
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Plasma - Ionosphere