**PHY ****401: Electrodynamics**** ****(4)**

*Prerequisites:* *PHY 305: Classical Mechanics, **PHY 301: Mathematical Methods I, PHY 302: Mathematical Methods II*

*Learning Objectives*:

Maxwell's equations will be discussed in detail with application to physical problem relating to electromagnetic fields including electromagnetic fields in the medium. Special relativity will be studied in context of Maxwell's equations, guage invariance and radiation by accelerating charged particles.

*Course Contents*:

Boundary problems, Formal solution with Green functions, Electric fields in matter, Boundary-Value problems with dielectrics, polarizability and susceptibility, Energy density in a dielectric, Multipole expansion.

Vector potential, Magnetic fields of a localized current distribution, Magnetic moment, Force and Torque on and energy of a localized current distribution, Boundary conditions on B and H, Boundary value problems in magnetostatics, Multipole expansion.

Maxwell equations, Gauge transformations, Green functions for the wave equation, Poynting's theorem, Tranformation properties of electromagnetic fields and sources under rotations, spatial reflections, and time reversal

Plane electromagnetic waves and wave propagation, polarization, Stokes parameters, Reflection and refraction of electromagnetic waves at a plane interface between dielectrics, wave propagation in conductors and dielectrics, dispersion, complex refractive index, waveguides

Fields and radiation of a localized oscillating source, Electric dipole fields and radiation, Linear antennas.

Scattering at long wavelengths, Rayleigh scattering

Minkowski space and four vectors, concept of four-velocity, Four acceleration and higher rank tensors, Relativistic formulation of electrodynamics, Maxwell equations in covariant form, Gauge invariance and four-potential, the action principle and electromagnetic energy momentum tensor, LiĆ©nard-Weichert potentials, Radiation from an accelerated charge, Larmor formula, bremsstrahlung and synchrotron radiation, multipole radiation, dispersion theory, radiative reaction, radiative damping.

*Suggested Books*:

- J. D. Jackson,
*Classical Electrodynamics*. - D. J. Griffiths,
*Introduction to Electrodynamics*, 3rd Ed. - L. D. Landau and E. M. Lifschitz,
*Classical Theory of Fields*. - R. P. Feynman, R. B. Leighton and M. Sands,
*The Feynman Lecture of Physics*Vol 2. - W. K. H. Panofsky and M. Philips.
*Classical Electricity and Magnetism*. - W. R. Smythe,
*Static and Dynamic Electricity*.

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