UPKAR PRAKASHAN, AGRA-2

ByAnshul Gupta

&Dr. Surekha Tomar

© Publishers

Publishers

UPKAR PRAKASHAN(An ISO 9001 : 2000 Company)

2/11A, Swadeshi Bima Nagar, AGRA–282 002Phone : 4053333, 2530966, 2531101Fax : (0562) 4053330, 4031570E-mail : care@upkar.inWebsite : www.upkar.in

Branch Offices

4845, Ansari Road, Daryaganj, 1-8-1/B, R.R. Complex (Near Sundaraiah Park,New Delhi–110 002 Adjacent to Manasa Enclave Gate), Bagh Lingampally,Phone : 011–23251844/66 Hyderabad–500 044 (A.P.), Phone : 040–66753330

● The publishers have taken all possible precautions in publishing this book, yet ifany mistake has crept in, the publishers shall not be responsible for the same.

● This book or any part thereof may not be reproduced in any form byPhotographic, Mechanical, or any other method, for any use, without writtenpermission from the Publishers.

● Only the courts at Agra shall have the jurisdiction for any legal dispute.

ISBN : 978-93-5013-269-2

Price : 499·00(Rs. Four Hundred Ninety Nine Only)

Code No. 1551

Printed at : UPKAR PRAKASHAN (Printing Unit) Bye-pass, AGRA

Preface of the Revised Edition

This revised version of the book consists of material covering the latest syllabusprescribed by CSIR–UGC/GATE as well as other competitive examinations ofnational level. This book is remarkable for its comprehensive coverage.

One aspect in each area of the problems spans a wide spectrum of topics. Theproblems themselves are remarkable for their versatility in applying the physical lawsand principles, their up-to-date realistic situations and their scanty demand onmathematical skills.

The solutions presented generally just provide a guidance to solving the problems,rather than step by step manipulation, and leave much to the students to work out forthemselves, of which much is demanded of the basic knowledge in physics. Thus, thebook would provide an invaluable complement to the text books. International unitsare used whenever possible, but in order to conform to some of the problems,Gaussian units are also used. This in fact would give the student broader training andwider experience. Great pains have been taken to trace the logical steps from the firstprinciples to the final solutions. These efforts hopefully will enhance the value of thebook to students and teachers alike.

—Dr. Surekha Tomar

CCCCoooonnnntttteeeennnnttttssss

● Previous Year’s Solved Paper

Part–A● General Aptitude………………………………………………………………… 1–64

Part–B & CUnit-1

Basic Mathematical Methods……………………………………………….…… 65–150Unit-2

Classical Dynamics……………………………………………………………… 151–222Unit-3

Electromagnetics………………………………………………………………… 223–297Unit-4

Quantum Physics and Applications………………………………………...…… 298–369Unit-5

Thermodynamic and Statistical Physics……………………………………..… 370–445Unit-6

Electronics…………………………………………………………,…………… 446–522Unit-7

Experimental Methods………………………………….……………,………… 523–558Unit-8

Atomic and Molecular Physics…………………………………………….…… 559–626Unit-9

Condensed Matter Physics……………………………………………………… 627–708Unit-10

Nuclear and Particle Physics…………………………………………………… 709–754Unit-11

Nature of Nuclear Forces………………………………………………..……… 755–770● Optics (Additional Reading),…………………………………………………… 771–776● Model Paper-I…...……………………………………………………………… 777–784● Model Paper-II…..……………………………………………………………… 785–792

GENERAL INFORMATION

EXAM SCHEMETime : 3 Hours Max. Marks : 200

Single Paper Test having Multiple ChoiceQuestions (MCQs) is divided in three parts.

Part 'A' This part shall carry 20 questions pertaining

to General aptitude with emphasis on logicalreasoning graphical analysis, analytical andnumerical ability, quantitative comparisons, seriesformation, puzzles etc. The candidates shall berequired to answer any 15 questions. Eachquestion shall be of two marks. The total marksallocated to this section shall be 30 out of 200.

Part 'B'This part shall contain 25 Multiple Choice

Questions (MCQs) generally covering the topicsgiven in the Part ‘B’ of syllabus. Candidates arerequired to answer any 20 questions. Eachquestion shall be of 3·5 marks. The total marksallocated to this section shall be 70 out of 200.

Part 'C'This part shall contain 30 questions from Part

‘C’ & ‘B’ of the syllabus that are designed to testa candidate's knowledge of scientific conceptsand/or application of the scientific concepts. Thequestions shall be of analytical nature where acandidate is expected to apply the scientificknowledge to arrive at the solution to the givenscientific problem. A candidate shall be requiredto answer any 20 questions. Each question shall beof 5 marks. The total marks allocated to thissection shall be 100 out of 200.● There will be negative marking @25% for

each wrong answer.

● To enable the candidates to go through thequestions, the question paper booklet shall bedistributed 15 minute before the scheduled

time of the Exam. The answer sheet (OMRsheet) shall be distributed at the scheduledtime of the Exam.

SYLLABUSPart 'A'

This part shall carry 20 questions pertainingto General aptitude with emphasis on logicalreasoning graphical analysis, analytical andnumerical ability, quantitative comparisons, seriesformation, puzzles etc. The candidates shall berequired to answer any 15 questions. Eachquestion shall be of two marks. The total marksallocated to this section shall be 30 out of 200.

Part 'B'I. Mathematical Methods of Physics

Dimensional analysis. Vector algebra andvector calculus. Linear algebra, matrices, Cayley-Hamilton Theorem. Eigenvalues and eigenvectors.Linear ordinary differential equations of first &second order, Special functions (Hermite, Bessel,Laguerre and Legendre functions). Fourier series,Fourier and Laplace transforms. Elements ofcomplex analysis, analytic functions; Taylor &Laurent series; poles, residues and evaluation ofintegrals. Elementary probability theory, randomvariables, binomial, Poisson and normal distri-butions. Central limit theorem.

II. Classical MechanicsNewton’s laws. Dynamical systems, Phase

space dynamics, stability analysis. Central forcemotions. Two body Collisions—scattering inlaboratory and Centre of mass frames. Rigid bodydynamics—moment of inertia tensor. Non-inertialframes and pseudoforces. Variational principle.Generalized co-ordinates. Lagrangian andHamiltonian formalism and equations of motion.

( vii )

Conservation laws and cyclic co-ordinates.Periodic motion: small oscillations, normalmodes. Special theory of relativity—Lorentztransformations, relativistic kinematics and mass–energy equivalence.

III. Electromagnetic Theory

Electrostatics : Gauss’s law and itsapplications, Laplace and Poisson equations,boundary value problems. Magnetostatics: Biot-Savart law, Ampere's theorem. Electromagneticinduction. Maxwell's equations in free space andlinear isotropic media; boundary conditions on thefields at interfaces. Scalar and vector potentials,gauge invariance. Electromagnetic waves in freespace. Dielectrics and conductors. Reflection andrefraction, polarization, Fresnel’s law, inter-ference, coherence and diffraction. Dynamics ofcharged particles in static and uniformelectromagnetic fields.

IV. Quantum Mechanics

Wave-particle duality. Schrödinger equation(time-dependent and time-independent).Eigenvalue problems (particle in a box, harmonicoscillator, etc.). Tunneling through a barrier.Wave-function in co-ordinate and momentumrepresentations. Commutators and Heisenberguncertainty principle. Dirac notation for statevectors. Motion in a central potential: orbitalangular momentum, angular momentum algebra,spin, addition of angular momenta; Hydrogenatom. Stern-Gerlach experiment. Time-inde-pendent perturbation theory and applications.Variational method. Time dependent perturbationtheory and Fermi's golden rule, selection rules.Identical particles, Pauli exclusion principle, spin-statistics connection.

V. Thermodynamic and Statistical Physics

Laws of thermodynamics and their con-sequences. Thermodynamic potentials, Maxwellrelations, chemical potential, phase equilibria.Phase space, micro and macro-states. Micro-canonical, canonical and grand-canonicalensembles and partition functions. Free energyand its connection with thermodynamic quantities.Classical and quantum statistics. Ideal Bose andFermi gases. Principle of detailed balance.Blackbody radiation and Planck's distribution law.

VI. Electronics and Experimental Methods

Semi-conductor devices (diodes, junctions,transistors, field effect devices, homo and hetero-junction devices), device structure, devicecharacteristics, frequency dependence andapplications. Opto-electronic devices (solar cells,photo-detectors, LEDs). Operational amplifiersand their applications. Digital techniques andapplications (registers, counters, comparators andsimilar circuits). A/D and D/A converters.Microprocessor and microcontroller basics. Datainterpretation and analysis. Precision andaccuracy. Error analysis, propagation of errors.Least squares fitting.

Part 'C'

I. Mathematical Methods of PhysicsGreen’s function. Partial differential

equations (Laplace, wave and heat equations intwo and three dimensions). Elements ofcomputational techniques: root of functions,interpolation, extrapolation, integration bytrapezoid and Simpson’s rule, Solution of firstorder differential equation using Runge-Kuttamethod. Finite difference methods. Tensors.Introductory group theory : SU(2), O(3).

II. Classical MechanicsDynamical systems, Phase space dynamics,

stability analysis. Poisson brackets and canonicaltransformations. Symmetry, invariance andNoether’s theorem. Hamilton-Jacobi theory.

III. Electromagnetic TheoryDispersion relations in plasma. Lorentz

invariance of Maxwell’s equation. Transmissionlines and wave guides. Radiation from movingcharges and dipoles and retarded potentials.

IV. Quantum MechanicsSpin-orbit coupling, fine structure. WKB

approximation. Elementary theory of scattering :phase shifts, partial waves, Born approximation.Relativistic quantum mechanics : Klein-Gordonand Dirac equations. Semi-classical theory ofradiation.

V. Thermodynamic and Statistical PhysicsFirst and second-order phase transitions.

Diamagnetism, paramagnetism and ferromag-netism. Ising model. Bose-Einstein condensation.

( viii )

Diffusion equation. Random walk and Brownianmotion. Introduction to non-equilibrium processes.

VI. Electronics and Experimental MethodsLinear and non-linear curve fitting, chi-square

test. Transducers (temperature, pressure/ vacuum,magnetic fields, vibration, optical and particledetectors). Measurement and control. Signalconditioning and recovery. Impedance matching,amplification (Op-amp based, instrumentationamp, feedback), filtering and noise reduction,shielding and grounding. Fourier transforms, lock-in detector, box-car integrator, modulationtechniques.

High frequency devices (including generatorsand detectors).

VII. Atomic & Molecular PhysicsQuantum states of an electron in an atom.

Electron spin. Spectrum of helium and alkaliatom. Relativistic corrections for energy levels ofhydrogen atom, hyperfine structure and isotopicshift, width of spectrum lines, LS & JJ couplings.Zeeman, Paschen-Bach & Stark effects. Electronspin resonance. Nuclear magnetic resonance,chemical shift. Frank-Condon principle. Born-Oppenheimer approximation. Electronic,rotational, vibrational and Raman spectra ofdiatomic molecules, selection rules. Lasers :spontaneous and stimulated emission, Einstein A& B coefficients. Optical pumping, populationinversion, rate equation. Modes of resonators andcoherence length.

VIII. Condensed Matter PhysicsBravais lattices. Reciprocal lattice. Diffraction

and the structure factor. Bonding of solids. Elastic

properties, phonons, lattice specific heat. Freeelectron theory and electronic specific heat.Response and relaxation phenomena. Drudemodel of electrical and thermal conductivity. Halleffect and thermo-electric power. Electron motionin a periodic potential, band theory of solids :metals, insulators and semi-conductors.Superconductivity : type-I and type-II super-conductors. Josephson junctions. Superfluidity.Defects and dislocations. Ordered phases ofmatter : translational and orientational order,kinds of liquid crystalline order. Quasi crystals.

IX. Nuclear and Particle Physics

Basic nuclear properties : size, shape andcharge distribution, spin and parity. Bindingenergy, semi-empirical mass formula, liquid dropmodel. Nature of the nuclear force, form ofnucleon-nucleon potential, charge-independenceand charge-symmetry of nuclear forces. Deuteronproblem. Evidence of shell structure, single-particle shell model, its validity and limitations.Rotational spectra. Elementary ideas of alpha, betaand gamma decays and their selection rules.Fission and fusion. Nuclear reactions, reactionmechanism, compound nuclei and direct reactions.

Classification of fundamental forces.Elementary particles and their quantum numbers(charge, spin, parity, isospin, strangeness, etc.).Gellmann-Nishijima formula. Quark model,baryons and mesons. C, P, and T invariance.Application of symmetry arguments to particlereactions. Parity non-conservation in weakinteraction. Relativistic kinematics.

Physical SciencesCSIR-UGC NET/JRF Exam.

Solved Paper

June 2013Physical Sciences

PART A

1. There is an equilateral triangle in the XYplane with its centre at the origin. Thedistance of its sides from the origin is 3·5 cm.The area of its circumcircle in cm2 is—(A) 38·5 (B) 49(C0 63·65 (D) 154

2. A sphere of iron of radius R/2 fixed to oneend of a string was lowered into water in acylindrical container of base radius R to keepexactly half the sphere dipped. The rise in thelevel of water in the container will be—

(A) R/3 (B) R/4(C) R/8 (D) R/12

3. A crystal grows by stacking of unit cells of10 × 20 × 5 nm size as shown in the diagramgiven below. How many unit cells will makea crystal of 1 cm3 volume ?

5 nm10 nm

20 nm

Unit Cell (not to scale)

10 nm5 nm 20 nm

Crystal (not to scale)

(A) 106 (B) 109

(C) 1012 (D) 1018

4. What is the value of 1

1 × 2 +

12 × 3

+ 1

3 × 4 +

… to ∞ ?

(A) 2/3 (B) 1

(C) 2 (D) ∞

5. A solid cylinder of basal area A was helddipped in water in a cylindrical vessel ofbasal area 2A vertically such that a length hof the cylinder is immersed. The lower tip ofthe cylinder is at a height h from the base ofthe vessel. What will be the height of water inthe vessel when the cylinder is taken out ?

h

h

(A) 2h (B)32 h

(C)43 h (D)

54 h

6. Of all the triangles that can be inscribed in asemicircle of radius R with the diameter asone side, the biggest one has the area—

(A) R2 (B) R2√⎯ 2

(C) R2√⎯ 3 (D) 2R2

7. Choose the largest number—

(A) 2500 (B) 3400

(C) 4300 (D) 5200

8. A daily sheet calendar of the year 2013contains sheets of 10 × 10 cm size. All thesheets of the calendar are spread over thefloor of a room of 5m × 7·3 m size. What

CSIR-UGC NET/JRF/SET PhysicalSciences.

Publisher : Upkar Prakashan ISBN : 9789350132500 Author : Anshul Gupta & Dr.Surekha Tomar

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