TS Ed CET 2020

Part – C

PHYSICAL SCIENCES Physics Syllabus ( 50 Marks)

1. Vector Analysis : Scalar and vector fields, gradient of a scalar field and its physical

significance. Divergence and curl of a vector field and related problems. Vector integration,

line, surface and volume integrals. Stokes, Gauss and Greens theorems- simple applications.

2. Mechanics of Particles : Laws of motion, motion of variable mass system, motion of a

rocket, multi-stage rocket, conservation of energy and momentum. Collisions in two and three

dimensions, concept of impact parameter, scattering cross-section,

3. Mechanics of rigid bodies: Definition of Rigid body, rotational kinematic relations,

equation of motion for a rotating body, angular momentum and inertial tensor. Euler‘s

equation, precession of a top, Gyroscope,

4. Central forces: Central forces – definition and examples, conservative nature of central

forces, conservative force as a negative gradient of potential energy, equation of motion under

a central force, gravitational potential and gravitational field, motion under inverse square law,

derivation of Kepler‘s laws, Coriolis force and its expressions.

5. Special theory of relativity: Galilean relativity, absolute frames, Michelson-Morley

experiment, Postulates of special theory of relativity. Lorentz transformation, time dilation,

length contraction, addition of velocities, mass-energy relation. Concept of four vector

formalism.

6. Fundamentals of vibrations: Simple harmonic oscillator, and solution of the differential

equation– Physical characteristics of SHM, torsion pendulum, – measurements of rigidity

modulus , compound pendulum, measurement of ‗g‘, combination of two mutually

perpendicular simple harmonic vibrations of same frequency and different frequencies,

Lissajous figures

7. Damped and forced oscillations: Damped harmonic oscillator, solution of the differential

equation of damped oscillator. Energy considerations, comparison with undamped harmonic

oscillator, logarithmic decrement, relaxation time, quality factor, differential equation of forced

oscillator and its solution, amplitude resonance, velocity resonance. Coupled Oscillators.

8. Vibrating Strings: Transverse wave propagation along a stretched string, general solution of

wave equation and its significance, modes of vibration of stretched string clamped at ends,

overtones, energy transport, transverse impedance

9. Vibrations of bars: Longitudinal vibrations in bars- wave equation and its general solution.

Special cases (i) bar fixed at both ends ii) bar fixed at the midpoint iii) bar free at both ends iv)

bar fixed at one end. Transverse vibrations in a bar- wave equation and its general solution.

Boundary conditions, clamped free bar, free-free bar, bar supported at both ends, Tuning fork.

10. Kinetic theory of gases: Introduction – Deduction of Maxwell‘s law of distribution of

molecular speeds, Transport Phenomena – Viscosity of gases – thermal conductivity –

diffusion of gases.

11. Thermodynamics: Basics of thermodynamics-Kelvin‘s and Claussius statements –

Thermodynamic scale of temperature – Entropy, physical significance – Change in entropy in

reversible and irreversible processes – Entropy and disorder – Entropy of universe –

Temperature- Entropy (T-S) diagram – Change of entropy of a perfect gas-change of entropy

when ice changes into steam.

12. Thermodynamic potentials and Maxwell’s equations: Thermodynamic potentials –

Derivation of Maxwell‘s thermodynamic relations – Clausius-Clayperon‘s equation –

Derivation for ratio of specific heats – Derivation for difference of two specific heats for

perfect gas. Joule Kelvin effect – expression for Joule Kelvin coefficient for perfect and

Vanderwaal‘s gas.

13. Low temperature Physics: Joule Kelvin effect – liquefaction of gas using porous plug

experiment. Joule expansion – Distinction between adiabatic and Joule Thomson expansion –

Expression for Joule Thomson cooling – Liquefaction of helium, Kapitza‘s method – Adiabatic

demagnetization – Production of low temperatures – Principle of refrigeration, vapour

compression type.

14. Quantum theory of radiation: Black body-Ferry‘s black body – distribution of energy in the

spectrum of Black body – Wein‘s displacement law, Wein‘s law, Rayleigh-Jean‘s law –

Quantum theory of radiation – Planck‘s law – deduction of Wein‘s distribution law, RayleighJeans law, Stefan‘s law from Planck‘s law.

Measurement of radiation using pyrometers – Disappearing filament optical pyrometer –

experimental determination – Angstrom pyroheliometer – determination of solar constant,

effective temperature of sun.

15. Statistical Mechanics: Introduction, postulates of statistical mechanics. Phase space, concept

of ensembles and some known ensembles ,classical and quantum statistics and their

differences, concept of probability, Maxwell-Boltzmann‘s distribution law -Molecular energies

in an ideal gas- Maxwell-Boltzmann‘s velocity distribution law, Bose-Einstein Distribution

law, Fermi-Dirac Distribution law, comparison of three distribution laws, Application of B-E

distribution to Photons-planks radiation formula, Application of Fermi-Dirac statistics to white

dwarfs and Neutron stars.

16. Interference: Principle of superposition – coherence – temporal coherence and spatial

coherence – conditions for Interference of light

Interference by division of wave front: Fresnel‘s biprism – determination of wave length of

light. Determination of thickness of a transparent material using Biprism – change of phase on

reflection – Lloyd‘s mirror experiment.

Interference by division of amplitude: Oblique incidence of a plane wave on a thin film due

to reflected and transmitted light (Cosine law) – Colours of thin films – Non reflecting films–

interference by a plane parallel film illuminated by a point source – Interference by a film with

two non-parallel reflecting surfaces (Wedge shaped film) – Determination of diameter of wire-

Newton‘s rings in reflected light with and without contact between lens and glass plate,

Newton‘s rings in transmitted light (Haidinger Fringes) – Determination of wave length of

monochromatic light – Michelson Interferometer – types of fringes – Determination of

wavelength of monochromatic light, Difference in wavelength of sodium D1,D2 lines and

thickness of a thin transparent plate.

17. Diffraction: Introduction – Distinction between Fresnel and Fraunhoffer diffraction

Fraunhoffer diffraction:- Diffraction due to single slit and circular aperture – Limit of

resolution – Fraunhoffer diffraction due to double slit – Fraunhoffer diffraction pattern with N

slits (diffraction grating)

Resolving Power of grating – Determination of wave length of light in normal and oblique

incidence methods using diffraction grating.

Fresnel diffraction-Fresnel‘s half period zones – area of the half period zones –zone plate –

Comparison of zone plate with convex lens – Phase reversal zone plate – diffraction at a

straight edge – difference between interference and diffraction.

18. Polarization: Polarized light : Methods of Polarization, Polarization by reflection, refraction,

Double refraction, selective absorption , scattering of light – Brewster‘s law – Malus law –

Nicol prism polarizer and analyzer – Refraction of plane wave incident on negative and

positive crystals (Huygen‘s explanation) – Quarter wave plate, Half wave plate – Babinet‘s

compensator – Optical activity, analysis of light by Laurent‘s half shade polarimeter.

19. Aberrations and Fiber Optics: Introduction – Monochromatic aberrations, spherical

aberration, methods of minimizing spherical aberration, coma, astigmatism and curvature of

field, distortion. Chromatic aberration – the achromatic doublet – Removal of chromatic

aberration of a separated doublet.

Fiber Optics : Introduction – Optical fibers –Principles of fiber communication – Step and

graded index fibers – Rays and modes in an optical fiber – Fiber material – Types of optical

fibers and advantages of fiber communication,

20. Electrostatics: Electric Field:- Concept of electric field lines and electric flux, Gauss‘s law

(Integral and differential forms), application to linear, plane and spherical charge

distributions. Conservative nature of electric field E, irrotational field. Electric Potential:-

Concept of electric potential, relation between electric potential and electric field, potential

energy of a system of charges. Energy density in an electric field. Calculation of potential

from electric field for a spherical charge distribution.

21. Magnetostatics :Concept of magnetic field B and magnetic flux, Biot-Savart‘s law, B due to a

straight current carrying conductor. Force on a point charge in a magnetic field. Properties of

B, curl and divergence of B, solenoidal field. Integral form of Ampere‘s law, applications of

Ampere‘s law: field due to straight, circular and solenoidal currents. Energy stored in

magnetic field. Magnetic energy in terms of current and inductance. Magnetic force between

two current carrying conductors. Magnetic field intensity. Ballistic Galvanometer:- Torque on

a current loop in a uniform magnetic field, working principle of B.G., current and charge

sensitivity, electromagnetic damping, critical damping resistance.

22. Electromagnetic Induction: Faraday‘s laws of induction (differential and integral form),

Lenz‘s law, self and mutual Induction. Continuity equation, modification of Ampere‘s law,

displacement current, Maxwell equations.

23. Electromagnetic waves: Maxwell‘s equations in vacuum and dielectric medium, boundary

conditions, plane wave equation: transverse nature of EM waves, velocity of light in vacuum

and in medium, polarization, reflection and transmission. Polarization of EM waves,

Brewster‘s angle, description of linear, circular and elliptical polarization.

24. Atomic Spectra and Models Inadequacy of classical physics: Brief Review of Black body

Radiation , Photoelectric effect, Compton effect, dual nature of radiation, wave nature of

particles. Atomic spectra, Line spectra of hydrogen atom, Ritz Rydberg combination

principle. Alpha Particle Scattering, Rutherford Scattering Formula, Rutherford Model of

atom and its limitations, Bohr‘s model of H atom, explanation of atomic spectra, correction

for finite mass of the nucleus, Bohr correspondence principle, limitations of Bohr model,

discrete energy exchange by atom, Frank Hertz Expt. Sommerfeld’s Modification of Bohr‘s

Theory.

Wave Particle Duality de Broglie hypothesis, Experimental confirmation of matter wave,

Davisson Germer Experiment, velocity of de Broglie wave, wave particle duality,

Complementarity. Superposition of two waves, phase velocity and group velocity, wave

packets ,Gaussian Wave Packet , spatial distribution of wave packet, Localization of wave

packet in time. Time development of a wave Packet; Wave Particle Duality,

Complementarity. Heisenberg Uncertainty Principle, Illustration of the Principle through

thought Experiments of Gamma ray microscope and electron diffraction through a slit. Time

independent and time dependent Schrodinger wave equation. Estimation of ground state

energy of harmonic oscillator and hydrogen atom, non-existence of electron in the nucleus.

Uncertainty and Complementarities.

Nuclear Physics Size and structure of atomic nucleus and its relation with atomic weight;

Impossibility of an electron being in the nucleus as a consequence of the uncertainty principle.

Nature of nuclear force, NZ graph, Liquid Drop model: semi-empirical mass formula and

binding energy, Nuclear Shell Model and magic numbers.

Radioactivity: stability of the nucleus; Law of radioactive decay; Mean life and half-life; Alpha

decay; Beta decay- energy released, spectrum and Pauli’s prediction of neutrino; Gamma ray

emission, energy-momentum conservation: electron-positron pair creation by gamma photons

in the vicinity of a nucleus. Fission and fusion- mass deficit, relativity and generation of

energy; Fission – nature of fragments and emission of neutrons. Nuclear reactor: slow neutrons

interacting with Uranium 235; Fusion and thermonuclear reactions driving stellar energy (brief

qualitative discussions), Classification of Elementary Particles

25. Basic Electronics: Classification of solids in terms of forbidden energy gap. Intrinsic and

extrinsic semiconductors, Fermi level, continuity equation – p-n junction diode, half wave

and full wave rectifiers and filters, ripple factor, Characteristics of Zener diode and its

application as voltage regulator. – p n p and n p n transistors, current components in

transistors, CB,CE and CC configurations – concept of transistor biasing, operating point,

fixed bias and self-bias transistor as an amplifier — concept of negative feedback and

Positive feedback – Barkhausen criterion.

2 6 . D i g i t a l P r i n c i p l e s: Binary number system, converting Binary to Decimal and vice versa.

Binary addition and subtraction (1s‘ and 2’s complement methods). Hexadecimal number

system. Conversion from Binary to Hexadecimal – vice versa and Decimal to Hexadecimal vice

versa. Logic gates: OR, AND, NOT gates, truth tables, NAND, NOR as universal gates,

Exclusive – OR gate, De Morgan’s Laws – statement and proof, Half and Full adders.

27. Quantum Mechanics: de Broglie’s hypothesis — wavelength of matter waves, properties of

matter waves, Properties of matter waves Phase and group velocities. Davisson and Germer

experiment. Double slit experiment. Standing de Brogile waves of electron in Bohr orbits.

Heisenberg’s uncertainty principle for position and momentum (x and px), Energy and time (E

and t). Gamma ray microscope. Diffraction by a single slit. Position of electron in a Bohr orbit.

Particle in a box. Complementary principle of Bohr. Schrodinger time independent and time

dependent wave equations. Wave function properties — Significance. Basic postulates of

quantum mechanics. Operators, Eigen functions and Eigen values, expectation values. Application

of Schrodinger wave equation to particle in one and three dimensional boxes, potential step and

potential barrier.

28. Nuclear Physics: Basic properties of nucleus — size, charge, mass, spin, magnetic dipole

moment and electric quadrupole moment. Binding energy of nucleus, deuteron binding

energy, p-p and n-p scattering (concepts), nuclear forces. Nuclear models — liquid drop model,

shell model. Range of alpha particles, Geiger — Nuttal law. Gammow’s theory of alpha decay.

Geiger — Nuttal law from Gammow’s theory. Beta spectrum — neutrino hypothesis,

Fermi’s theory of 13 —decay.

29. Solid State Physics: Crystalline nature of matter. Crystal lattice, Unit Cell, Elements of

symmetry. Crystal systems, Bravais lattices. Miller indices. Simple crystal structures (S.C.,

BCC, CsCI, FCC, NaCI diamond and Zinc Blends)

Diffraction of X —rays by crystals, Bragg’s law, and Experimental techniques – Laue’s method

and powder method.

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