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Old April 13th, 2015, 10:34 AM
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Default BHU M. Sc entrance exam Syllabus

I want to get BHU M. Sc Physics entrance exam Syllabus for doing preparation of this exam so will you please provide me that ?
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Old April 13th, 2015, 03:07 PM
Nitin Sharma
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Default Re: BHU M. Sc entrance exam Syllabus

As you want to get BHU M. Sc Physics entrance exam Syllabus for doing preparation of this exam so here I am giving you same:

UNIT I Coordinates Systems: Curvilinear coordinates: orthogonal curvilinear coordinates; rectangular, spherical and cylindrical polar coordinates. Velocity, acceleration and volume element in spherical polar coordinates.

Mechanics of a Single and of System of Particles: Newton’s laws of motion, Mechanics of a Particle, Equation of motion of a particle ( simple cases; motion of a particle subject to a resistive force, motion of a projectile in a resisting medium), Mechanics of a system of particles; angular momentum and energy of a system. Motion of a system with variable mass.

Motion in a central force field: Equivalent one body problem, equations of motion in central force field and their solutions. Motion in an inverse square law force field , Equation of the orbit; elliptical hyperbolic and parabolic orbits. Kepler’s laws of planetary motion and their derivations

UNIT II Collision of Particles: Elastic and inelastic scattering. Elastic scattering: laboratory and centre of mass systems, kinematics of elastic scattering. Inelastic scattering. Cross section ;differential cross section , impact parameter, the Rutherford formula.
Lagrangian Formulation : Constraints, Generalized coordinates, D’Alembert’s principle. Lagrangian equations, general expression for kinetic energy, Lagrangian of some simple systems (simple pendulum, spherical pendulum, charged particle in an electromagnetic field).

Moving coordinate systems : Rotating coordinate systems. The Coriolis force, motion on the Earth, effects of Coriolis force on a freely falling particle.

Oscillations: Simple harmonic oscillator; energy of a simple harmonic oscillator, compound pendulum, mass attached to a spring. Damped harmonic oscillator;Energy dissipation. Forced oscillations; Amplitude resonance.

UNIT III Special Theory of Relativity: Newtonian relativity. Michelson-Morley experiment, special theory of relativity, Lorentz Tranformations and their consequences ( Relativity of simultaneity,Lorentz-FitzGerald length contraction , time dilation. Relativistic addition of velocities; variation of mass with velocity, mass energy relation. Space-time four-dimensional continuum, four-vectors.

UNIT IV Vector Calculus: Scalar and Vector Fields, Triple Vector Product, The operator , Laplacian operator, Gradient of a Scalar and its geometrical interpretation, Divergence and Curl of Vector, Physical interpretation of Curl and Divergence. Line, Surface and Volume integrals, Evaluation of double and triple integrals. The fundamental theorem for gradients, Gauss’s Divergence Theorem, Stoke’s Theorem.

Electrostatics: Multipole Expansion of E for Distribution of Charge at Rest, Dipole and Quadrupole Fields, Electrostatic Field Energy, Force per unit area on the surface of a conductor in an electric field, Point Charge in front of a Grounded Plane Infinite Conductor. Dielectrics: Parallel Plate Capacitor with a Dielectric, Dielectric Constant, Polarization and Polarization Vector P, Displacement Vector D, Relation Between E, P & D, Boundary Conditions Satisfied by E and D at the interface between two Homogenous Dielectrics, Illustration Through Simple Examples.

UNIT V Current Electricity: Steady Current, Current Density J, Non-Steady Currents and Continuity Equation, Rise and Decay of Current in LR and RC circuits, Decay Constants, Transients in LCR Circuits, AC circuits, Complex Numbers and their applications in solving AC circuit problems, Complex Impedance and Reactance, Series and Parallel Resonance, Q factor, Power Consumed by an AC circuit, Power Factor.

Magnetostatics: Magnetic Dipole Moment, Biot -Savart’s law, Ampere’s Circuital Law, .B = 0,  x B =  0 J, Magnetization Current, Magnetization Vector, H Field (magnetizing field), Calculation of H in Simple Geometrical Situations (Hystersis Loop, Rowland ring) Susceptibility and Magnetic Permeability (linear cases). Faraday’s Laws, Integral and Differential Forms, Energy in a Static Magnetic Field, Maxwell’s Displacement Current, Maxwell’s Equations, Electromagnetic Field Energy Density. The wave equation satisfied by E and B, Plane Electromagnetic Waves in Vacuum, Poynting Vector and Theorem, Reflection and Refraction at a Plane Boundary of Dielectrics.

UNIT VI Kinetic theory: Basic concepts, Degrees of freedom, Equipartition of energy. Specific heat of monatomic diatomic and tri-atomic gases, behaviour at low temperatures, Maxwell’s velocity distribution, distribution of speeds ; mean values.

Transport phenomena in gases: Molecular collisions, mean free path and collision cross section. Transport Phenomenon: transport of momentum, mass and energy and their inter-relationship. Brownian motion, Einstein’s theory.
Deviation from perfect gas behaviour, van der Waals’ equation of state, nature of Vander Waals forces, comparison with experimental results, the critical constants. Joules expansion of ideal gas and of a Vander Waals gas, Joule coefficient, estimates of J-T cooling.

Liquefaction of gases: Boyles temperature and inversion temperature, principle of regenerative cooling and of cascade cooling, Liquification of hydrogen and helium, refrigeration cycles, meaning of efficiency. Cooling due to adiabatic demagnetization.

UNIT VII Thermodynamics:Concept of thermal equilibrium, internal energy. Carnot theorem. Entropy, Principle of increase of entropy, the thermodynamic scale of temperature, its identity with the perfect gas scale, impossibility of attaining the absolute zero, Third law of thermodynamics.

Thermodynamic relationships: Thermodynamic variables ; Extensive and Intensive, Maxwell’s general relationship. Clausius-Clapeyron heat equation, thermodynamic potentials and equilibrium of thermodynamical systems, relation with thermodynamical variables.

The Statistical basis of thermodynamics: Probability and Thermodynamic probability, Probability distribution. The expressions for average properties, constraints , accessible and inaccessible states, distribution of particles with a given total energy into discrete set of energy states; microstates and macrostates.

Probability and entropy: Boltzmann Entropy relation, Statistical interpretation of the second law of thermodynamics, Boltzmann Canonical distribution law ; partition function, partition function of an ideal monoatomic gas. The rigorous form of Equipartition of energy. Maxwell-Boltzmann ,Fermi-Dirac and Bose-Einstein Statistics( Derivation of distribution laws in each case).

UNIT VIII Transverse waves on an ideal stretched string; The wave equation, general solution of one dimensional wave equation; harmonic waves, Standing waves on a string of fixed length, energy of a vibrating string.

Longitudinal waves in a solid: The wave equation for longitudinal waves on a thin cylindrical rod, energy density and energy transmission in waves. Application to Earthquakes.

Waves over liquid surface: concept of gravity waves and ripples. Group velocity and phase velocity.

Two dimensional waves: Standing waves on a stretched rectangular membrane: solution by method of separation of variables, normal modes of vibrations.

Interference of light: The principle of superposition, two-slit interference, Intensity distribution, Displacement of fringes. Interference in thin parallel films.Non-reflecting films. Michelson interferometer, its application for precision determination of wavelength,
wavelength difference and width of spectral lines. Multiple beam interference, Fabry-Perot interferometer and etalon; Intensity distribution.

UNIT IX Fraunhofer diffraction: diffraction at a slit, the intensity distribution. Diffraction at a circular aperture. Two slit diffraction pattern, intensity distribution.

Diffraction gratings: Diffraction at N parallel slits, intensity distribution at an N parallel slits.Plane diffraction grating Resolution of images, Rayleigh criterion, resolving power of telescopic and microscopic systems, resolving power of a grating . Frensel diffraction: Frensel half-period zones, The Zone-Plate. Diffraction at a circular aperture, Diffraction by a straight edge (analysis using half-period zones). Rectilinear propagation of light.

Polarization: Polarization by reflection, Malus’s law. Double refraction, Refraction in Uniaxial crystals.Optical activity, Rotation of plane of polarization.Origin of optical rotation in liquids and in crystals.

Unit X Origin of quantum theory: Black body radiation; Planck’s radiation law, Photoelectric effect, Compton Effect.

Wave properties of particles: De-Broglie’s matter wave, the concept of wave packets and group velocities, evidence for diffraction and interference of particles, Davison-Germer Experiment, Heisenberg’s uncertainty relation for p and x, its extension to energy and time, applications of uncertainty principle.

Quantum mechanics: Schrödinger’s wave equation (Time independent form), linearity and superposition, expectation values, operators.

Applications: particle in a box, finite potential well, tunnel effect, harmonic oscillator.

Quantum Theory of Hydrogen atom: Schrödinger equation for Hydrogen atom, separation of variables, Quantum numbers ( n, l, m), space quantization, electron probability density.

Unit XI Atomic Structure: Electron spin, Stern-Gerlach experiment, Pauli’s exclusion principle, symmetric and anti-symmetric wave functions, atomic structures (shells and sub-shells). Spin-orbit coupling, total angular momentum J, L-S coupling, j-j coupling;Term-symbols Normal and anomalous Zeeman Effect, Lande g-factor. The molecular bond, mechanism of electron sharing, the hydrogen molecule.

Diatomic molecules: Quantization of rotational energies; rotational energy levels, pure rotational spectra .Vibrational energy levels, pure vibrational spectra. Rotation-Vibration spectra of diatomic molecules.

Raman Effect: Stokes and anti-Stokes lines, classical theory of Raman-effect, Raman-activity (concept of Polarizability ellipsoid).

Unit XII Structure of Nuclei: Nuclear composition, nuclear properties(size, spin, magnetic moment), Stable Nuclei ( Nuclear decay, Binding energy), Liquid drop model, Shell model. Meson theory of nuclear forces.

Radioactive decay: Half-life, radioactive series. Theory of Alpha decay ( Tunneling effect) , beta-decay, gamma- decay.

Nuclear Reactions: Cross section, Nuclear Fission, Nuclear reactors. Nuclear Fusion; Nuclear Fusion in Stars, Fusion reactor.

Elementary particles: Interaction and particles, Classification;Leptons and hadrons,Elementary particle quantum numbers;Baryon,lepton and strangeness numbers. Quarks; colour, flavour, quark confinement.

Unit XIII The crystalline state; crystal lattice,the unit cell, Bravais lattice and seven crystal systems. Point groups, space groups , non- Bravais lattice. Crystal planes and Miller indices. Simple crystal structures; Sodium Chloride, Diamond, Zinc sulfide. Amorphous solids.Interatomic forces,Types of bonding( ionic,covalent,metallic,hydrogen,van der Waals) Reciprocal lattice and X-ray diffraction, The diffraction condition, Bragg’s law. Experimental techniques; the rotating-crystal method, the Laue method, the powder method.

Lattice vibrations: Elastic waves, density of states of continuous medium. Specfic heat; Einstein and Debye models.Lattice waves; the one-dimensional monoatomic lattice,density of states of a lattice. The concept of Phonons.

Unit XIV Motion of electrons: Quantum mechanical free electron gas, Electrical conductivity, electrical resisitivity versus temperature, Heat capacity of conduction electrons. The Fermi surface; electrical conductivity ( effects of the Fermi surface),thermal conductivity in metals.

Band Structure: Energy bands in solids; the Bloch theorem, Electrons in one dimensional periodic potential, concept of Brillouin zones, explanation of energy bands on the basis of Brillouin zones. Metals, insulators and semiconductors.

Semiconductor theory: Band structure, intrinsic semiconductors; temperature dependence of carrier concentration. Impurity states ( acceptor and donor), extrinsic semiconductors; the electron-hole concentration product. Electrical conductivity; temperature dependence. The effect of magnetic field on a semiconductor; the Hall effect.

Unit XV
Semiconductor Devices: p-n junction, working (on the basis of energy band diagram), rectification property, derivation of rectification equation. The junction transistor, its working (on the basis of energy band diagram), Tunnel diode, the Field effect transistor.

Pn-junction diode, Zener diode as a voltage regulator. bridge rectifier, ripple factor,passive filters, regulated power supply.
Transistor load line, Transistor biasing techniques (Voltage divider),bias stability, thermal runaway.

Transisitor equivalent circuits, h-parameters; h-parameter equivalent circuit for CE configuration,. FET and its characteristics, MOSFET; types and characteristics , applications of MOSFET.

Transistor amplifiers, Two-stage RC coupled amplifier; equivalent circuit at mid-frequency,Gain at mid –frequency., Transformer coupled amplifiers, expression of gain at mid-frequency. Emitter follower.
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