Electromagnetism 3230

Program for exam 2009

 

  1. Electrostatic

•        Coulomb’s law for a static electric field E

•        Gauss’s theorem; its applications

a.      Spherically symmetrical charge distribution

b.     Cylindrical distribution of charge

c.      Charge distributed homogeneously over a plane (capacitor as an example)

•        Maxwell’s equations for the static electric field

•        Scalar potential V, its relation with the static electric field E

a.      Poisson’s equation for the potential

b.     Solution of the Poisson’s equation in an integral form

  1. Magnetostatic

•        Maxwell’s equation for a static magnetic field

a.      Gauss’s law

b.     Ampere’s law

•        Integral form of the Ampere’s law; its applications to

a.      The field produced by a long linear wire with current

b.     The field inside the solenoid

c.      The field outside of the solenoid

•        Vector potential A, its relation with the magnetic field B

•        Current conservation law

•        Poisson’s equation for the vector potential

a.      Solution of the Poisson’s equation for the vector potential in an integral form

•        Bio-Savart law

  1. Maxwell’s equations for E and B in general case (time-dependent)

•        Gauss’s law for electric and magnetic fields

•        Ampere’s law (with the Maxwell’s term)

•        Faraday’s law

•        Current conservation; relation between the Maxwell’s equations and the current conservation law

•        Integral forms of the Maxwell’s equations

  1. Scalar and vector potentials V, A

•        Relations between the potentials V, A and fields E, B

•        Gauge transformations for the potentials

a.       gauge invariance of the fields and classical equations of motion of charged particles

b.     Lorentz gauge

c.      equations for the potentials, which follow from the Maxwell’s equations

  1. Wave equation in the vacuum

•        Wave equation for the potentials (in the Lorentz gauge)

•        Wave equation

a.      general properties of the wave equation;

b.     general form of the solution which depends on x and t ; retardation; velocity of the wave propagation

c.      monochromatic solutions, plane waves

•        Wave equation for the potentials V, A

•        Wave equation for the fields E, B

a.      linear polarization

b.     circular polarization

c.      velocity of light

  1. Force, which the fields E, B produce on charges
  2. Ohm’s law
  3. Applications of the Faraday’s law

•        Relation between the flux of the magnetic field and the emf, which  it produces

a.      two sources for the emf production

o      variation of the magnetic field

o      variation of the geometry

  1. Energy of the electromagnetic field

•        Energy of magnetic field

•        Energy as a function of A and j

•        General expression for the energy in terms on B

•        Energy of the electric field

•        Energy of a capacitor

•        Energy as a function of V,

•        Energy as a function of E

•        Total energy of the EM field

  1. Maxwell’ equations in matter

•        Charges and currents produced by polarization P; conservation of the polarization current

•        Current related to magnetization M

•        Fields D, H, their relation to E, B, P, M

•        Linear media; electric and magnetic susceptibility and permeability

•        Boundary conditions for E, B, D, H

  1. Conservation of energy in the EM field, the Poynting theorem
  2. Conservation of momentum in the EM field, the Maxwell’s stress tensor
  3. Angular momentum of the electromagnetic field
  4. Electromagnetic waves in insulators; refraction index, its relation to the electric and magnetic permeabilities
  5. Dispersion and absorption
  6. A simple model, which describes the behaviour of atoms and molecules in the electromagnetic field, which explains

•        the origin of the dispersion and its relation to the absorption

•        the role of resonances in these processes

•        the behaviour of the refraction index in the vicinity of a resonance

  1. Wave packets; the phase and group velocity of EM waves, dependence of these velocities on the index of refraction
  2. The reflection on the boundary between the two media for the normal incidence.
  3. Electromagnetic waves in metals

•        Maxwell’s equations in metals

•        Wave-type solution of the Maxwell’s equations

•        Electric permeability and the refraction index for metals; their dependence on frequency

•        Good and poor metals

•        Penetration of the EM wave into the metal, the skin effect

•        Reflection of the wave on the metal surface for normal incidence

  1. Radiation of electromagnetic waves

•        The electric dipole approximation (E1)

•        Behaviour of electric and magnetic fields produced by a time-dependent electric dipole at large distances

•        The flux of radiated energy in the dipole approximation

•        Angular distribution of the dipole radiation

•        Polarization of the dipole radiation

•        Energy rate radiated by an electric dipole

•        The case of an electric dipole, which oscillates with the given frequency

  1. Scattering of the low-frequency electromagnetic waves by atoms and molecules (in a gas). Dependence of the flux of the scattered wave on the frequency. (This topic was discussed very briefly on the last lecture. Correspondingly, only a basic knowledge is required.)