Given : (the almost-Maxwell equations [AME]), div D = rho, div B = 0, curl E = -dB/dt, and curl H = J

• write down the expression for the flux of a vector V
• write down the divergence theorem (which has to do with the flux of a vector V)
• write down the expression for the circulation of a vector V
• write down Stokes' theorem (which has to do with the circulation of a vector V)
• write down the continuity equation (which has to do with the conservation of charge)
• identify the origin of each of the AME (coulomb's law, gauss's law, etc.)
• write downs the full set of Maxwell equations
• show that the AME are not consistent with the equation of continuity
• Show that the full set of Maxwell equations are consistent with the equation of continuity

• Start from the integral of E dot J over a volume, and derive poynting's theorem. Identify the meaning of each term in Poynting's theorem.
• show that Eo exp( i k dot r - iwt) represents a travelling plane wave
• show that the travelling plane wave above satisfies the free-space wave equation
• from Maxwell's equations
• derive the free-space wave equation for the electric field
• show for a travelling plane wave in E that E is perpendicular to k the propagation vector
• show for a travelling plane wave in B that B is perpendicular to k the propagation vector
• show for travelling E and B plane waves that E is perpendicular to B
• show for travelling E and B plane waves that E and B are in phase
• show for travelling E or B plane waves that v = omega/k
• show for travelling E and B plane waves that E x B lies in the direction of k
• show that k in a medium = 2 pi n/lambda, where lambda is the vacuum wavelength and n is the index of refraction in the medium
• For plane waves incident obliquely on a plane boundary between dielectric materials, reason carefully from from the constancy of the phase at the boundary (and using a labelled, intelligible diagram) that
• angle of incidence = angle of reflection
• snell's law holds: n1 sin theta1 = n2 sin theta 2
• identify the four boundary conditions to be satisfied by the field vectors at the interface of two dielectric, non-magnetic materials. Be able to derive two of these from Maxwell's equations.
• show the reflected plane-wave E field at normal incidence from n1 to n2 is inverted when n2>n1 and not when n2<n1
• for even or odd slab waveguide modes, draw a clear diagram and work out the condition to be satisfied by the x-component of the propagation vector at x=+a. This must show exactly how the boundary conditions are brought into play.

• problems from exams 1 and 2
• given static E, calculate V, or given static V calculate E
• problems with a charge in the presence of a conducting sphere or grounded conducting plane or both
• problems involving gauss's law (spherical, plane, or cylindrical geometry)
• problems involving linear dielectrics (calculate D, E, P, V)
• near a sphere, or between spherical shells
• between conducting plates in one or more layers
• in a finite layer between (maybe partially filling ) the space between coaxial infinitely long conducting cylinders
• derive the electric field near a 'point' electric dipole from V(dipole) = k p dot r/r^3
• no calculations with Biot-Savart law or Ampere's law
• no problems involving a charge near an infinite plane boundary between two dielectric media (images with dielectrics)