Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Electrodynamics Instructor: Prabuddha Chakraborty Room: G26 Level: Undergraduate Time: Currently offered |
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Syllabus Past Exams Syllabus: i) Brief review of vector calculus. Physical interpretation of gradient, divergence and curl; Statement and physical interpretations of Greens theorem, Gauss divergence theorem, Stokes curl theorem. Differential forms (in R3); gradient, divergence, curl as co-boundaries (ds) of differential forms (in R3); Statement of Stokes theorem for differential forms (in R3); Greens theorem, the divergence theorem, the curl theorem as special cases (Generalized Fundamental Theorem of Calculus). Spherical coordinates; Cylindrical coordinates. Dirac delta function in in one/two/three dimensions; Delta function as divergence of a radially outward vector field; Justification for treating Dirac delta as a function; Remarks on Schwartzs distribution theory. Vector fields and potentials. ii) Electrostatics. Coulombs Law for discrete and continuous charge distributions; Divergence and curl of electrostatic fields. Electric potential; Poissons equation and Laplaces equation; Electrostatic Boundary Conditions; General remarks on Greens function (Impulse response). Work and Energy in Electrostatics. Conductors; Surface Charge and the Force on a Conductor; Capacitors. iii) Potential and field due to arrangement of charges. Solution to Laplaces equation; Harmonic Functions; Mean-value property; Illustration in One Dimension, Two Dimensions, Three Dimensions. Boundary Conditions and Uniqueness Theorems for Laplaces equation; Application to conductors. iv) The Method of Images. Separation of variables. Multipole Expansion; Monopole and Dipole terms; The Electric Field of a Dipole. Dielectrics; Polarization; Electric displacement. v) Magnetostatics. Lorentz Force Law; Magnetic fields; Currents. Biot-Savart Law; Steady Currents; Magnetic Field of a Steady Current. Divergence and Curl of Magnetic field; Amperes Law; Maxwells Equations for Electrostatics and Magnetostatics. Magnetic vector potential. vi) Electromotive Force; Ohms Law. Electromagnetic Induction; Faradays Law; Inductance; Energy in magnetic field. Maxwells correction to Amperes law for magnetodynamics; Maxwells Equations - differential and integral form; The Conundrum of Magnetic Charge/Monopole. vii) Conservation Laws; The Continuity Equation; Poyntings work-energy theorem of electrodynamics. Maxwells Stress Tensor; Conservation of Momentum. Electromagnetic Waves. The Wave Equation; Sinusoidal Waves; General remarks on the Fourier transform; Polarization. ElectromagneticWaves in Vacuum; The Wave Equation for E and B; Monochromatic Plane Waves; Energy and Momentum in Electromagnetic Waves. viii) Special Theory of Relativity from Maxwells electrodynamics; Einsteins thoughtexperiment and postulates. Relativity of simultaneity; Time dilation; Lorentz length contraction. The Lorentz group of transformations; The Structure of Spacetime; The Lorentz Metric; Space-time diagrams. Remarks on magnetism as a relativistic phenomenon. Reference Texts: (a) Introduction to Electrodynamics - D. J. Griffiths. (b) Foundations of Electromagnetic theory - J. R. Reitz, F. J. Milford andW. Charisty. (c) (Chapter 5) A Visual Introduction to Differential Forms and Calculus on Manifolds - J. P. Fortney. (d) Theory and Problems of Electromagnetics (Schaums Outlines) - J. A. Edminister. (e) A Guide to Physics Problems part 1: Mechanics, Relativity and Electrodynamics - S. B. Cahn and B. E. Badgorny. Evaluation:
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