The Dirac Delta Function: Review of vector calculus using example of Dirac Delta function, the divergence of r/r2, the one-dimensional and the three-dimensional Dirac delta functions. The theory of vector fields: the Helmoholtz theorem, potentials.

Electrostatics: The electric field: introduction, Coulomb’s law, the electric field, continuous charge distributions. Divergence and curl of electrostatic fields: field lines, flux and Gauss’s law, the divergence of E, applications of Gauss’s law, the curl of E. Electric potential: introduction to potential, comments on potential, Poisson’s equation and Laplace’s equation, the potential of a localized charge distribution, summary; electrostatics boundary conditions, Work and energy in electrostatics: the work done to move a charge, the energy of a point charge distribution, the energy of a continuous charge distribution, comments on electrostatic energy. Conductors: basic properties, induced charges, surface charge and the force on a conductor, capacitors.

Special Techniques: Laplace’s equation: introduction, Laplace’s equation in one, two and three dimensions, boundary conditions and uniqueness theorems, conductors and second uniqueness theorems.

The Method of Images: The classic image problem, induced surface charge, force and energy, other image problems

Separation of Variables: Cartesian coordinates spherical coordinates.

Multipole Expansion: Approximate potential at large, the monopole and dipole terms, origin of coordinates in multipole, expansions, the electric field of a dipole.

Electric Fields in Matter: Polarization: dielectrics, induced dipoles, alignment of polar molecules, polarization. The field of a polarized object: bound charges, physical interpretation of bound charges, and the field inside a dielectric. The electric displacement: Gauss’s law in the presence of dielectrics, a deceptive parallel, boundary conditions. Linear Dielectrics: susceptibility, permittivity, dielectric constant, boundary value problems with linear dielectrics, energy in dielectric systems, forces on dielectrics.

Magnetostatics: The Lorentz Force law: magnetic fields, magnetic forces, currents. The Biot-Savart Law: steady currents, the magnetic field of a steady current. The divergence and curl of B: straight-line currents, the divergence and curl of B, applications of Ampere’s law, comparison of magnetostatics and electrostatics. Magnetic Vector Potential: the vector potential, summary; magnetic boundary conditions, multipole expansion of the vector potential.

Magnetic Fields in Matter: Magnetization: diamagnets, paramagnets, ferromagnets, torques and forces on magnetic dipoles, effect of a magnetic field on atomic orbits, magnetization. The Field of a Magnetized Object: bound currents, physical interpretation of bound currents, and the magnetic field inside matter. The auxiliary field H: Ampere’s law in magnetized materials, a deceptive parallel, boundary conditions. Linear and nonlinear media: magnetic susceptibility and permeability, ferromagnetism.

Recommended Text:
1. D. J. Griffiths, “Introduction to Electrodynamics”, 3rd Edition, Prentice Hall (1999).
2. Mathew N. O. Sadiku,”Elements of Electromagnetics”, 2nd Edition, Oxford University Press (1995).
3. F. Melia, “Electrodynamics”, University of Chicago Press, (2001).
4. Hearld J and W. Muller-Kristen, “Electrodynamics”, World Scientific Publishing (2004).