**Lalit Narayan Mithila University, Darbhanga B.Sc. part-1 Physics Honours syllabus –**

**Paper-I, and Paper-II**

There will be two theory papers, each of three hours duration and will carry 75 marks of each paper. There will be one practical paper of 50 marks of three hours duration.

__Paper-I__Five questions to be answered. Question number 1 will have six short type questions, out of which three will have to be answered. There will be four questions each from Group A and Group B. Two questions from each Group will have to be answered, besides question number one which will be compulsory. The questions will be of equal value.

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**Group-A**

**Mathematical Physics and Properties of Matter**

Infinite sequence and series-convergence and divergence, Functions of several variables-partial differentiation, Taylor’s series, multiple integrals, random variables and probabilities-statistical expectations value, variance, analysis of random errors, probability distribution functions (Binomial, Gaussian and Poisson).

Transformation Properties of vectors, Differentiation and integration of vectors; Line integral, volume integral and surface integral involving vector fields; Gradient, divergence, and curl of a vector field, Gauss’s divergence theorem, Stokes theorem, Green’s theorem-application to simple problem; Orthogonal curvilinear co-ordinate systems, unit vectors in each system, illustration by plane, spherical and cylindrical co-ordinate systems only.

The relation between elastic constants, twisting torque on a cylinder of wire. Bending of the beam, cantilever, and flat spiral spring. Kinematics of moving fluids, poiseuille’s equation for the flow of a liquid through a capillary tube, viscosity, experimental determination of coefficient of the viscosity of a liquid, Rankine’s method for measuring the viscosity of the gas, surface tension, and surface energy, excess pressure inside an air bubble, measurement of surface tension by ripple’s method.

**Group-B**

**Special theory of relativity, Oscillations, Waves, and acoustics**

Michelson-Morley experiments and it’s an outcome, postulates of the special theory of relativity, Lorentz transformation, simultaneity and order of events, length contraction, time dilation, the relativistic transformation of velocity, relativistic addition of velocity, the variation of mass with velocity, mass-energy equivalence, relativistic Doppler Effect.

Damped and forced Oscillations, critical damping, resonance, waves in a one-dimensional chain of particles, classical wave equation, and waves in continuous media, energy transmission in waves, group velocity and phase velocity.

Fourier analysis and its applications, the intensity of sound waves, acoustic of building, reverberation, Sabine’s formula.

__Paper-II__Five questions to be answered. Question number 1 will have six short type questions, out of which three will have to be answered. There shall be four questions each from group A and group B. Two questions from each group will have to be answered, besides question number 1 which will be compulsory. The questions will be of equal value.

**Group-A**

**Thermal Physics**

**Kinetic theory of gases:**Basic assumptions of Kinetic theory, Ideal gas approximation, deduction of perfect gas laws. Maxwell’s distribution law (both in terms of velocity and energy), root mean square and most probable speeds.

**Finite-size of molecules:**Collision probability. Distribution of free paths and mean free path from maxwell’s distribution. Degrees of freedom, equipartition of energy (detailed derivation not required).

**Transport Phenomena:**Viscosity, thermal conduction, and diffusion of gases, Brownian motion; Einstein’s theory, Perrin’s work determination of Avogadro number.

**Real gases:**Nature of intermolecular interaction, Isotherms of real gases. Vander-Waals equation of state, critical constants of gas, the law of corresponding states, Virial coefficients, Boyle’s temperature.

**Conduction of Heat:**Thermal conductivity, diffusivity, Fourier’s equation for heat conduction-its solution for the rectilinear and radial (spherical and the cylindrical) flow of heat.

**Radiation:**Spectral emissive and absorptive powers, Kirchoff’s law blackbody radiation, energy density, radiation pressure, Stefan Boltzman law, Wein’s displacement law, Rayleigh-Jeans law, Planck’s law (no detailed derivation).

**Basic Concepts:**Microscopic and mac point of view thermodynamic variables of a system, State function. Exact and inexact differentials.

**First Law of Thermodynamics:**Thermal equilibrium. Zeroth law and the concept of temperature. Thermodynamic equilibrium internal energy. external work, Qu static process, the first law of thermodynamics and applications including magnetic systems, specific heats and their ratio, isothermal and adiabatic changes in perfect and real gases.

**The second law of thermodynamics:**Reversible and irreversible processes, indicator diagram. Carnot’s cycles-efficiency, Carnot’s theorem, Kelvin’s scale of temperature, relation to perfect gas scale. second law of thermodynamics-different formulations and their equivalence, Clauses inequality, entropy change of entropy in simple reversible and irreversible processes, entropy, and disorder, equilibrium and entropy principle, principle of degradation of energy.

**Thermodynamic Functions:**Enthalpy, Helmholtz and Gibbs free energies, Legendre transformations, Maxwell’s relations and simple deductions using these relations, thermodynamic equilibrium, and free energies.

Change of State Equilibrium between phases, triple point, Gibb’s phase rule (statement only) and simple applications. First and higher-order phase transitions, Ehrenfest criterion. Clausius-Clapeyronn’s equation. Joule Thomson effect, Temperature of inversion.

**Group-B**

**Electrostatics and Magnetism**

**Gauss’ law: Coulomb’s law of electrostatics.**The intensity and potential theorem-its application, Poisson and Laplace’s equation Superposition theorem (statement only) Application of Laplace equation to simple cases of the symmetric spherical charge distribution.

**Multi-pole expansion:**Multi pole expansion of scalar potential: mono-pole, dipole and quadric-pole terms: potential and field due to a dipole: work is done in deflecting a dipole: dipole-dipole interaction (for both electric and magnetic dipoles): force on dipole in a non- homogenous field.

**Dielectrics Polarization, electric displacement vector (D):**Gauss theorem in dielectric media: boundary conditions: electrostatic field energy: computation of capacitance in simple cases (parallel plates): spherical and cylindrical capacitors containing dielectrics-uniform and non-uniform, the relation between three electric vectors.

**Electrical images:**Solution of field problem in case of a point charge near a grounded conducting an infinite plane. Boundary value problem in the uniform external field for

**(i)**conducting spherical shell and dielectric sphere.

**Magnetic effect of steady current:**Magnetic field B. Magnetic force between current elements and definition of B. Magnetic flux Biot-Savart’s law B due to the straight current-carrying conductor and

**(ii)**current loop. Current loop as a magnetic dipole and its dipole moment (analogy with electric dipole), Ampere’s circuital law (integral and differential forms) B due to a Properties of B, Curl, and Divergence of B. Vector potential. Forces on an isolated moving charge, Magnetic force on a current-carrying wire, Torque on a current loop in a uniform magnetic field.

**Magnetic Properties of Matter:**Magnetism of matter: Gauss’s l of magnetism (integral and Differential forms). Magnetization current, Relative permeability of a material, Magnetic susceptibility Magnetization vector (M), Magnetic intensity (H); Relation between B, M, and H. The stored magnetic energy in matter, Magnetic circuit. BH curve and energy loss in hysteresis.

**Electromagnetic induction:**Faraday’s law (Differential and integral forms), Lenz’s law. Self and mutual induction. Energy stored in a magnetic field.

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__LNMU B.Sc. part-1 Physics subsidiary syllabus__

__LNMU B.Sc. part-1 Physics subsidiary syllabus__

**Lalit Narayan Mithila University, Darbhanga B.Sc. part-1 physics (subsidiary) Syllabus**

There shall be one theory paper of three hours duration carrying 75 marks beside one practical paper of three hours duration carrying 25 marks.

**Theory Paper**

The question paper will consist of three groups. Group A will have six short type questions out of which three will have to be answered. Group B and C will have four questions out of which two questions will have to be answered from each group. Question number one will be compulsory.

**Group-A**

There will be only

**one**question from this group, which will be compulsory. Six short type questions from topics in Group B and C will be asked. Examinees will be expected to answer any five of them.**Group-B**

Mathematical Physics, STTR, Mechanics, General Properties of Matter, Waves, oscillations, and Acoustics

**Mathematical Physics:**Vector algebra, addition, subtraction and multiplication of vectors. Gradient, Divergence, Curl and Laplacian operations.

Special Theory of Relativity: Galilean Transformation, Inertial frame of reference. Michelson Morley experiment, Lorentz-Fitzerald contraction. Einstein postulates. Lorentz Transformation and its consequences. Length contraction and time dilation.

Addition of velocities. Relativistic variation of mass with velocity mass-energy relation.

**Mechanics and General Properties of the matter:**Kepler’s laws of planetary motion, elasticity and elastic constants bending of the beam. Determination of young’s modulus. Cantilever, torsion and rigidity modulus. Flat spiral spring. Effect of temperature and pressure on elasticity, Bernoulli’s theorem. The viscosity of liquids.

Critical velocity, Poisseule’s formula with correction, capillary tube flow, the effect of temperature and pressure on viscosity. Surface tension and surface energy. Ripple and gravity waves. Determination of surface tension by the method of ripples.

**Waves, oscillations, and Acoustics:**The differential equation of waves, Equation of a progressive wave, stationary wave, compression waves in fluids and extended solids. Free, damped and forced oscillations, Fourier analysis. Intensity and loudness of the sound and their measurement, Acoustics of building. Ultrasonics.

**Group-C**

**Thermal Physics, Computer Fundamentals, and Electronics**

**Thermal Physics:**Perfect gas equation, Vander Waals equation of state, Maxwell’s law of distribution of velocity, Joule Thomson effect, Liquefaction of gases with special reference to Helium, Transport phenomenon of gases, Mean free path, The laws of thermodynamics, Carnot engine and Carnot cycle, Thermodynamic relations and their applications to simple physical problems, entropy, the principle of increase of entropy, the thermodynamic scale of temperature, Kirchoff’s law and black body radiation Stefan’s law, Wien’s law, Rayleigh-Jeans law, Planck’s law.

**Computer Fundamentals:**Basic components of a computer and their functions, Types of a computer system, Number system, decimal, binary, octal and hexadecimal system and their arithmetic.

**Basic Electronics**: p-n junction diode, forward and reverse bias, half-wave, and full-wave rectifiers, Zener diode, a photodiode, LED