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Summary |
Notes |
1 |
Static electric and magnetic fields
- Laws of electrostatics and magnetostatics in free space, in the integral form
- Lorentz force and relativity
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2 |
Revision of vector calculus
- Definitions of gradient, divergence and curl
- Del and Laplace operators
- Useful theorems of vector calculus
- Laws of electrostatics and magnetostatics in the differential form
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3 |
Electric and magnetic dipoles
- Electric dipole moment; electric dipoles
- Dipole potential and electric field
- Dipoles in uniform and non-uniform external fields
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4 |
Ideal conductors; electrostatic problems
- Ideal conductors in the electrostatic field
- Laplace and Poisson equations of electrostatics
- General problem of electrostatics; the uniqueness theorem
- The method of image charges
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5 |
Magnetostatics; electromagnetic induction
- Poisson equations of magnetostatics
- Magnetic dipoles
- Qualitative discussion of induced currents
- Faraday's law of electromagnetic induction
- Electromotive force in a loop of wire
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6 |
Maxwell's equations in free space
- The continuity equation
- Modification of Ampere's law for non-steady currents
- The displacement current
- Maxwell's equations of electrodynamics in free space
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7 |
Dielectric materials
- Polarisation of dielectric materials
- Polarisation charges and polarisation currents
- LIH materials; electric susceptibility
- Susceptibility for gaseous dielectrics
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8 |
Electric field in dielectric materials
- The electric displacement field D; relative permittivity
- Gauss's law for the D field
- Boundary conditions for the E and D fields
- E and D field lines at boundaries
- Energy density of the electric field
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9 |
Diamagnetism and paramagnetism
- Magnetic properties of atoms; the Bohr magneton
- Magnetisation and magnetic susceptibility
- Microscopic theory of diamagnetism and paramagnetism
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10 |
Magnetic field in materials (part 1)
- Surface and volume magnetisation currents
- The auxiliary H field
- Maxwell-Ampere law for the H field
- Example: a permanent magnet
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11 |
Magnetic field in materials (part 2)
- Relative permeability of materials
- Boundary conditions for the B and H fields
- Energy density of the magnetic field
- Ferromagnetism; hysteresis
- Electromagnets
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12 |
Electromagnetic waves in free space
- Wave equations in free space
- General solutions to the wave equations
- Monochromatic plane wave solutions
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13 |
EM waves in dielectrics; Poynting vector
- Properties of monochromatic plane waves in vacuum and dielectrics
- Wave impedance
- EM energy flux: the Poynting vector
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14 |
Polarisation of plane waves
- Energy flux in a monochromatic plane wave
- Linear, circular and elliptic polarisations
- Absorptive linear polarisers; Malus's law
- Circular polarisers: quarter-wave plates
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15 |
Dispersion of waves in dielectrics
- Classical thoery of dispersion
- Complex refractive index
- Propagation and absorption of waves in dielectrics
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16 |
EM waves at boundaries of dielectrics
- Boundary conditions for monochromatic waves
- Reflection and refraction
- Critical angle; total internal reflection
- Evanescent fields
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17 |
The Fresnel equations
- S and P polarisations of plane waves
- Derivation of the Fresnel equations
- Main properties of the Fresnel coefficients
- Brewster's angle
- Energy transport at boundary
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18 |
Low-frequency EM waves in conductors
- Ohm's law; conductivity in the low-frequency regime
- Wave number in conductors
- Definition of good conductors
- Refractive index in good conductors
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19 |
Low-frequency EM waves in good conductors
- Wave attenuation in good conductors
- Wave impedance in good conductors
- Reflection at vacuum/good conductor boundary
- Skin effect
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20 |
EM waves in plasma
- Plasma oscillations, plasma frequency
- Refractive index of plasma
- Dispersion relation in plasma
- Properties of EM waves in plasma
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21 |
Motion of charges in uniform fields
- Motion in uniform electric and magnetic fields
- Cyclotron frequency and radius
- Principles of mass spectrometry
- Thomson's parabola spectrometer
- Electrostatic lenses (non-uniform field)
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22 |
Transmission lines and waveguides
- Transmission lines
- Wave propagation in a parallel wire line
- Wave propagation in a rectangular waveguide
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