PHYSICS 315 Electromagnetic Theory I
- vector analysis
- divergence and curl of vector fields
- vector identities
- integral calculus
- line, surface and volume integrals of vector fields
- Stoke's theorem
- the divergence theorem
- Green's identities
- curvilinear coordinates
- plane polar coordinates
- cylindrical coordinates
- spherical polar coordinates
- electrostatics
- Dirac delta in curvilinear coordinates
- electric field and Coulomb's law
- electric flux and Gauss' law
- applications of Gauss' law
- differential form of Gauss' law
- curl of the electrostatic field
- electrostatic potential
- work done on a charge displaced in an electric field
- electric potential calculations for different charge configurations
- electric potential gradient from centre to rim on a uniformly charged disk
- electrostatic energy of charge distributions, energy density
- Laplace's and Poisson's equations
- Solution of Laplace's equation by separation of variables
- rectangular boxes or pipes with specified potentials on the boundaries
- potential inside a cylindrical box with specified potentials on the lateral, top and bottom surfaces
- spherical geometries with azimuthal symmetry, Legendre polynomials
- potential due to a sphere with specified potential (or charge density) on the surface
- electric potential and charge density near a corner or edge of a conductor
- spherical conductor immersed in a uniform electric field
- method of images
- point charge close to a grounded conducting plane
- point charge near a grounded conducting sphere
- multipole expansion of the electrostatic potential
- monopole, dipole, quadrupole approximations at large distances
- electric field of a dipole
- quadrupole moment calculations of various charge distributions
- dielectric media
- polarisation; surface and volume polarisaton charge densities
- Gauss' law in a linear dielectric, electric displacement field
- electric permittivity, susceptibility and dielectric constant in polarizable media
- electrostatic energy in dielectrics
- boundary conditions on electric and displacement field vectors across an interface
- boundary value problems involving dielectrics
- field of a uniformly (or radially) polarised sphere
- a dielectric sphere placed in an otherwise uniform electric field
- a long dielectric cylinder placed in a uniform electric field that is normal to its axis
- method of images for dielectric interfaces
- electric current
- current density, equation of continuity
- Ohm's law, conductivity, resistivity
- resistance calculations
- charge decay in a conductive medium
- introduction to magnetostatics
- Lorenz force
- Biot-Savart law
- divergence and curl of the magnetic field
- magnetic vector potential; its relation to current density
- multipole expansion of the vector potential
- magnetic moment calculations