5th Semester
PHY-501 Methods of Mathematical Physics-I 3 (3 – 0)
Vector operations, Physical significance of DEL operator, Gauss’s divergence theorem, Green’s theorem, Stokes’s theorem, Orthogonal curvilinear coordinates system, Gradient, Divergence, Curl and Laplacian in orthogonal curvilinear coordinates, Spherical polar and Cylindrical coordinates systems. Complex numbers, Euler’s formula, De Moivre’s theorem, elementary functions, analytic functions of complex variables, CauchyRiemann equation, harmonic functions, complex integration, Cauchy’s theorem, Cauchy’s integral formula, Taylor and Laurent series, Contour integrals, singularities and residues, residue theorem, branch points and integrals of multivalued functions. Tensors Analysis and applications.Recommended Books:
1. Arfken G.B and H.J Weber, F.E Harris, 2012, 7th Edition, Mathematical Methods for Physicists, A. Press, New York.
2. Dass H.K, R. Verma, 2011, 6th Edition, Mathematical Physics, S. Chand& Company Ltd. New Delhi.
3. Kreyszig E. 2011, 10th Edition, Advanced Engineering Mathematics. Wiley, New York.
4. Collins R.E, 2011, 2nd Edition, Mathematical Methods for Physicists and Engineers, Dover Publications.
5. Tang K.T, 2010, 2nd Edition, Mathematical Methods for Engineers and Scientists 2, Springer.
6. Spiegel M.R 2009, 1st EditionAdvanced Mathematics for Engineers and Scientists, Schaum’s outlines series, McGraw Hill.
7. Riley K F, M P Hobson and S J Bence. 2006, 3 rd Edition, Mathematical Methods for Physics and Engineering, Cambridge University Press, Cambridge.
PHY-503 Classical Mechanics 3 (3 – 0)
Historical development of classical mechanics, Newtonian mechanics of single particle & system of particles, constraints, generalized coordinates, D’Alembert’s Principle , Derivation of Lagrange’s equations, simple applications of the lagrangian formulation, Hamilton’s Principle, Techniques of the calculus of variation, Derivation of Lagrange’s equation from Hamilton’s principle, Applications of Hamilton’s principle, shortest distance between two points in a plane and space, minimum surface of revolution, the Brachistochrone problem, conservation theorem , Two body central force problem & its reduction to the equivalent one body problem, Kepler’s law as an inverse square law problem, Differential equation for the orbits and the different shapes of the orbit, planetary orbits & their equations, Legendre transformations and its applications, Derivation of Hamilton’s equation of motion, Hamiltonian, cyclic coordinates, Routh’s Procedure, The equations & examples of canonical transformations, Poisson’s brackets & their properties, Poisson’s brackets & other canonical invariants, Poisson’s theorem, invariance of Poisson’s bracket under canonical transformation. Recommended Books:1. Goldstein H, P Charle and J L Safko. 2001, Classical Mechanics. Addison-Wesley.
2. Hand L N and J.D Finch. 1998, Analytical Mechanics. Cambridge University Press, Cambridge.
3. Barger V D and M G Olsson. 1995, Classical Mechanics. McGraw-Hill, New York.
4. Landau L D and E M Lifshitz. Mechanics. 1960, Pergamon, Oxford.
5. Classical Mechanics by J.W. Leech Methuen and Co. Ltd., London, 1958.
PHY-505 Electrodynamics-I 3 (3 – 0)
Electric dipole, Electric field and electric potential at a point due to dipole, mutual interaction energy of two dipoles, Force and Couple on the dipole placed in an external electric field, Dielectrics: Polarization and polarization density vector, surface and volume charge densities due to polarization, electric field inside the dielectric, electric susceptibility and dielectric constant, Poisson and Laplace equations both for dielectric and space, Solution to Laplace equation in Cartesian, spherical and cylindrical coordinates, Uncharged conducting and dielectric sphere in uniform electric field, Electrostatic Images, Point charge near an infinite grounded conducting plane, Electric potential, electric field intensity and surface charge density in case of point charge and conducting sphere.Electric current: nature of electric current, current density, equation of continuity, Ohm’s law, steady current in media without source of e. m. f., Approach to electrostatic equilibrium, Magnetic properties of steady current: Current carrying element, Force on current carrying conductor, Biot-savart law and their applications, Ampere’s circuital law and their applications, Magnetic vector and scalar potential, Magnetic field of a distant circuit, Magnetic properties of matter: Magnetization vectors M, Magnetic current densities due to surface and volume currents and vector potential, Magnetic field due to the magnetized material, Magnetic scalar potential and pole density, Magnetic intensity vector H, Relation between H and M, Field equation, Magnetic susceptibility and permeability, Boundary conditions on the field vectors.Recommended Books:
1. Bo Thide, 2011, The Electromagnetic filed theory 2nd Ed.
2. Martin Dressed, 2002, Electrodynamics of solids (optional properties of electron in matter), 1st Ed. Cambridge University, Press.
3. Griffiths D.J. 1999, Introduction to Electrodynamics, 3rd Edition
4. John R. Reitz, 1992, Foundations of Electromagnetic Theory, 4th Edition
PHY-507 Electronics-I 3 (3 – 0)
Liner network analysis; superposition, Thevenin, Norton and Mill man’s theorems, Electronics: the p-n junction, Bias the p-n junction diode, diode, characteristics of diode, different models and types of diodes, halfwave and full-wave rectifier, full-wave bridge rectifier, capacitor, inductive, and πR filters, Clipping and clamping circuits, Zener voltage regulators, regulated power supply, varactor diodes, Optical diodes, Light emitting Diodes. Bipolar junction transistor (BJT), transistor characteristics, biasing circuits such as base bias, emitter bias, voltage-divider bias, feedback bias circuits, amplifier classifications, common emitter amplifier, the emitter followers, the common base amplifier. RC-coupled amplifiers, Power amplifiers, (class A, class B amplifiers, class C amplifier), introduction to Junction field-effect transistors (JFET), JFET biasing circuits, the common source follower, introduction to MOSFET.Recommended Books:
1. Floyd, T. L. 2010. Electronic Devices 9TH Ed. Prentice-Hall Intern. Inc., Englewood Cliffs (USA). 2. Nashelsky, L. & Robert, L. B. 2009. Electronic Devices and Circuit Theory 10TH Ed. Prentice-Hall Intern. Inc., Englewood Cliffs (USA).
3. Malvino, A. P. 2008. Electronic Principles. 7TH Ed. Glencoe-McGraw-Hill Book Co.
4. Grob, B. 2003. Basic Electronics 9TH Ed. McGraw-Hill
PHY-509 Relativity and Cosmology 3 (3 – 0)
Special Relativity, Galilean relativity, Einstein’s postulates of special relativity. Consequences of special relativity. Michelson-Morley experiment, Lorentz transformations, consequences of Lorentz transformations (the relativity of length, the relativity of time, concept of simultaneity) Relativistic Mechanics, Transformation of relativistic velocities, addition of relativistic velocities, Relativity of mass, Force equation in relativity, rest mass ,KE and total energy, conservation of energy and momentum, the conversion of mass to kinetic energy in Uranium Fission, pair production and annihilation, The Cerenkov Effect and Cerenkov radiation, Einstein’s mass-energy relationship and its practical examples, particle of Zero rest mass, Relativistic Doppler Effect, Aberration of Light, Tachyons, structure of space time, Geometry of space time, Minkowski space time tensors, the light cone, and four vectors (position four vector, four velocity, four momentum, four force). General relativity, Gravity as a Geometry, The equivalence principle, clocks in a gravitation field, space time is curved, geodesics, the geodesic equation, equation of geodesic deviation, Einstein field equation Manifolds and coordinates, curves and surfaces, tensor fields, metric tensor. Cosmology cosmological redshift, Hubble’s law, microwave background, the Big Bang, Theory, Historical background of universe, stars , neutron stars, pulsars , black holes, quasars, singularity, measuring the distance to stars, concept of open, closed and flat universe, dark matter(MACHOs and WIMPs-)Recommended Books:
1. James B. 2005, An Introdu ing to Einstein’s General Relativity. Hartle Pearson Education. 2. Beiser A. 2002. 6th E. Perspectives of Modern Physics. McGraw-Hill.
3. Resnick, Halliday and Krane. 2002, Physics Vol. I, 5th Ed. John Wiley and Sons Inc, New York.
4. McComb W D. 1999, Dynamics and Relativity. Oxford University Press.
5. Inverno R.D. Introducing Einstein’s Relativity.1992, Oxford University Press.
6. Narlikar J V. 1989, Introduction to Cosmology. Cambridge University Press.
PHY-511 Lab Course-III (Electromagnetism) 3 (0 – 3)
1. To determine the resistance of various DC conductors by recording their current/voltage characteristics.2. To study the internal resistance and matching in various voltage sources and draw their power diagrams.
3. Establishment of relationship between electrostatic force and charge, electrostatic force and distance between charges and to determine the electric constant using Coulomb’s Law / image charge.
4. To study the ferromagnetic hysterisis of a two ring-shaped iron cores by continuous adjustable direct current and to determine the remanence and coersive field strength.
5. Investigation of induced current and voltage in secondary coil of a transformer as a function of number of turns and current flowing in the primary coil.
6. To determine the inductance and phase displacement of coil (single, parallel and series formations) in AC circuit as a function of frequency of voltage source.
7. To determine the capacitance and phase displacement of capacitor (single, parallel and series formations) in AC circuit as a function of frequency of voltage source.
8. To determine the dielectric constants of different materials.
9. To study the ripple of the output voltage of various rectifier circuits as a function of the load current strength and the charging capacitance.
10. To study the frequency response of simple RC filters by point-by-point measurements and the sweep displayed on the oscilloscope.
11. To investigate the filter characteristics as a function of frequency of a coil, a capacitor, an Ohmic resistance and combinations of these components and to determine the phase displacement of the filters as a function of frequency.
12. To study the behavior of RLC series and parallel circuit and determination of its resonance frequency.(Optional: To determine the dielectric constant using RLC series circuit.)
Recommended Books:-
1. Kraftmakers, Y. 2007. Experiments and demonstrations in Physics, World Scientific Publishing Co. Ltd.
2. David J. Griffiths, Introduction to Electrodynamics, 3rd Edition
3. Isenberg, C. 1996. Physics Experiments and Projects for students (Physics experiments & Projects). Taylor and Francis, USA
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