Electrostatics: Continuous Charge Distribution, Delta Function,
Field and Potential, Poisson and Laplace's equations, Boundary
Conditions and Uniqueness theorems, Electrostatic potential energy,
Capacitance, Conductors.

Boundary Value Problems: Solution of Laplace and Poisson equations in 2
& 3 dimensions. Method of images, separation of variables in
Cartesian, Cylindrical and Spherical coordinate systems, Multipole
expansion, Green's function approach.

Dielectrics: Polarization, bound charges, susceptibility, energy and
force, boundary conditions, boundary value problems.

Magnetostatics: Biot-Savert's Law, Ampere's law, vector potential,
magnetic field, moments, force, torque and energy of localized current
distributions. Boundary conditions, boundary value problems.

Electrodynamics: Electromotive force, Ohm's law, Faraday's law, self
and mutual inductance, energy in magnetic fields, Maxwell's equations,
Gauge transformations, potential formulation, energy and momentum
conservation, Poynting theorem.

Electromagnetic Waves: Wave equation, Propagation of electromagnetic
waves in non conducting medium, reflection, transmission, Snell's law,
Brewster's angle, critical angle, Dispersion in non-conducting medium.

N |
Topic |
Lectures |
---|---|---|

1 | Coulomb's Law and Examples; Continuous charge distributions; Electric Field; Gauss Law | |

2 | Scalar Potential; Poisson and Laplace Equations; Integral Equation for electric potential; Boundary conditions and Uniqueness theorem; Formal Solution by Green's Function method. | |

3 | Electrostatic Energy; Continuous Charge distributions; Conductors and Capacitance | |

4 | Method of Images; Green's Functions for a spherical boundary surface | |

5 | Method of separation of variables; Function Spaces and bases; Two Dimensional Problems in rectangular and cylindrical geometries; | |

6 | Green's Functions in two dimensions | |

7 | Laplace equation in 3D; Spherical coordinates; Spherical Harmonics; | |

8 | Green's Functions in Spherical coordinates | |

9 | Multipole Expansion; Quadrupole moment tensors | |

10 | Dielectrics; Electric Displacement; Linear Dielectrics; Boundary Value Problems; Energy; | |

11 | Steady Currents; Biot-Savart Law; Magnetic Field; Ampere's Law | |

12 | Vector Potential; Multipole Expansion; Magnetic Dipoles; | |

13 | Magnetic Fields in Matter; Boundary Value Problems | |

14 | Faraday's Law; Inductance - Self and Mutual; Energy in Magnetic Fields | |

15 | Maxwell's Equations; Macroscopic version; Potentials; Gauge transformations; | |

16 | Conservation Laws; Energy Conservation and Poynting Theorem; Momentum conservation; Angular Momentum | |

17 | Electromagnetic Waves: Wave equation, Propagation of electromagnetic waves in non conducting medium, reflection, transmission, Snell's law, Brewster's angle, critical angle, Dispersion in non-conducting medium. | |

Additional topics
if time permits |
||

18 | Solution of Laplace equation by Numerical method and Variational method. | |

19 | Solution of two dimensional problems by conformal mapping. |