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# (Paper) Physics : Main Examination

**UPSC
: Physics : Main Examination**

**PAPER-I**

**Section-A**

**1. Classical Mechanics**

**(a) Particle dynamics**

Centre of mass and laboratory coordinates, conservation of linear and. angular
momentum. The rocket equation.. Rutherford scattering, Galilean transformation,
intertial and non-inertial frames, rotating frames, centrifugal and Coriolis
forces, Foucault pendulum.

**(b) System of particles**

Constraints, degrees of freedom, generalised coordinates and momenta. Lagranges
equation and applications to linear harmonic oscillator, simple pendulum and
central force problems. Cyclic coordinates, Hamilitonian Lagranges equation from
Hamiltons principle.

**(c) Rigid body dynamics**

Eulerian angles, inertia tensor, principal moments of inertia. Eulers equation
of motion of a rigid body, force-free motion of a rigid body. Gyroscope.

**2. Special Relativity,
Waves & Geometrical Optics**

**(a) Special Relativity**

Michelson-Morley experiment and its implications. Lorentz transformations-length
contraction, time dilation, addition of velocities, aberration and Doppler
effect, mass-energy relation, simple applications to a decay process. Minkowski
diagram, four dimensional momentum vector. Covariance of equations of physics.

**(b) Waves**

Simple harmonic motion, damped oscillation, forced oscillation and resonance.
Beats-. Stationary waves in a string. Pulses and wave packets. Phase and group
velocities. Reflection and Refraction from Huygens principle.

**(c) Geometrical Optics**

Laws of relfection and refraction from Fermats principle. Matrix method in
paraxial optic-thin lens formula, nodal planes, system of two thin lenses,
chromatic and spherical aberrations.

**3. Physical Optics**

**(a) Interference**

Interference of light-Youngs experiment, Newtons rings, interference by thin
films, Michelson interferometer. Multiple beam interference and Fabry-Perot
interferometer. Holography and simple applications.

**(b) Diffraction**

Fraunhofer diffraction-single slit, double slit, diffraction grating, resolving
power. Fresnel diffraction: - half-period zones and zones plates. Fresnel
integrals. Application of Cornus spiral to the analysis of diffraction at a
straight edge and by a long narrow slit. Diffraction by a circular aperture and
the Airy pattern.

**(c) Polarisation and Modern
Optics**

Production and detection of linearly and circularly polarised light. Double
refraction, quarter wave plate. Optical activity. Principles of fibre optics
attenuation; pulse dispersion in step index and parabolic index fibres; material
dispersion, single mode fibres. Lasers-Einstein A and B coefficients. Ruby and
He-Ne lasers. Characteristics of laser light-spatial and temporal coherence.
Focussing of laser beams. Three-level scheme for laser operation.

**Section-B**

**4. Electricity and
Magnetism**

**(a) Electrostatics and
Magnetostatics**

Laplace ad Poisson equations in electrostatics and their applications. Energy of
a system of charges, multipole expansion of scalar potential. Method of images
and its applications. Potential and field due to a dipole, force and torque on a
dipole in an external field. Dielectrics, polarisation. Solutions to
bounary-value problems-conducting and dielectric spheres in a uniform electric
field. Magentk shell, uniformly magnetised sphere. Ferromagnetic materials,
hysteresis, .energy loss.

**(b) Current Electricity**

Kirchhoffs laws and their applications. Biot-Savart law, Amperes law, Faradays
law, Lenz law. Self-and mutual-inductances. Mean and rms values in AC circuits.
LR CR and LCR circuits- series and parallel resonance. Quality factor. Principal
of transformer.

**5. Electromagnetic Theory
& Black Body Radiation**

**(a) Electromagnetic Theory**

Displacement current and Maxwells equatons. Wave equations in vacuum, Poynting
theorem. Vector and scalar potentials. Gauge invariance, Lorentz and Coulomb
gauges. Electromagnetic field tensor, covariance of Maxwells equations. Wave
equations in isotropic dielectrics, reflection and refraction at the boundary of
two dielectrics. Fresnels relations. Normal and anomalous dispersion. Rayleigh
scattering.

**(b) Blackbody radiation**
.

Balckbody radiation ad Planck radiation law- StefaivBoltzmann law, Wien
displacement law and Rayleigh-Jeans law. Planck mass, Planck length, Planck
time,. Planck temperature and Planck energy.

**6. Thermal and Statistical
Physics**

**(a) Thremo dynamics**

Laws of thermodynamics, reversible and irreversible processes, entropy.
Isothermal, adiabatic, isobaric, isochoric processes and entropy change. Otto
and Diesel engines, Gibbs phase rule and chemical potential, van der Waals
equation of state of a real gas, critical constants. Maxwell-Boltzman
distribution of molecular velocities, transport phenomena, equipartition and
virial theorems. Dulong-Petit, Einstein, and Debyes theories of specific heat of
solids. Maxwell lllrelations and applications. Clausius- Clapeyron equation.
Adiabatic demagnetisation, Joule-Kelvin effect and liquefaction of gases.

**(b) Statistical Physics**

Saha ionization formula. Bose-Einstein condenssation. Thermodynamic behaviour of
an ideal Fermi gas, Chandrasekhar limit, elementary ideas about neutron stars
and pulsars. Brownian motion as a random walk, diffusion process. Concept of
negative temperatures.

**PAPER-II**

**Section-A**

**1. Quantum Mechanics I**

Wave-particle dualitiy. Schroedinger equation and expectation values.
Uncertainty principle. Solutions of the one-dimensional Schroedinger equation
free particle (Gaussian wave-packet), particle in a box, particle in a finite
well, linear harmonic oscillator. Reflection and transmission by a potential
step and by a rectangular barrier. Use of WKB formula for the life-time
calcuation in the alpha-decay problem.

**2. Quantum Mechanics II
& Atomic Physics**

**(a) Quantum Mechanics II**

Particle in a three dimensional box, density of states, free electron theory of
metals. The angular meomentum problem. The hydrogen atom. The spin half problem
and properties of Pauli spin matrices.

**(b) Atomic Physics**

Stern-Gerlack experiment, electron spin, fine structure of hydrogen atom. L-S
coupling, J-J coupling. Spectroscopic notation of atomic states. Zeeman effect.
Frank-Condon principle and applications.

**3. Molecular Physics**

Elementary theory of rotational, vibratonal and electronic spectra of diatomic
molecules. Raman effect and molecular structure. Laser Raman spectroscopy
Importance of neutral hydrogen atom, molecular hydrogen and molecular hydrogen
ion in astronomy Fluorescence and Phosphorescence. Elementary theory and
applications of NMR. Elementaryideas about Lamb shift and its significance.

**Section-B**

**4. Nuclear Physics**

Basic nuclear properties-size, binding energy- angular momentum, parity,
magnetic moment. Semi-empirical mass formula and applications. Mass parabolas.
Ground state of a deuteron magnetic moment and noivcentral forces. Meson theory
of nuclear forces. Salient features of nuclear forces. Shell model of the
nucleus-success and limitations. Violation of parity in beta decay. Gamma decay
and internal conversion. Elementary ideas about Mossbauer spectroscopy. Q-value
of nuclear reactions. Nuclear fission and fusion, energy production in stars.
Nuclear reactors.

**5. Particle Physics &
Solid State Physics**

**(a) Particle Physics**

Classification of elementary particles and their interactions. Conservation
laws. Quark structure of hadrons. Field quanta of electroweak and strong
interactions. Elementary ideas about Unification of Forces. Physics of
neutrinos.

**(b) Solid State Physics**

Cubic crystal structure. Band theory of solids- conductors, insulators and
semiconductors. Elements of superconductivity, Meissner effect, Josephson
junctions and applications. Elementary ideas about high temperature
superconductivity.

**6. Electronics**

Intrinsic and extrinsic semiconductors-p-n-p and n-p-n transistors.Amplifiers
and oscillators. Op-amps. FET, JFET and MOSFET. Digital electronics-Boolean
identities, De; Morgans laws, Logic gates and truth tables., Simple logic
circuits. Thermistors, solar cells. Fundamentals of microprocessors and digital
computers.