SEMESTER III
PHYSICS-C V: MATHEMATICAL PHYSICS-II
(Credits: Theory-04) Theory: 60 Lectures
Mid Semester: 15 End Semester: 60 Full Marks: 75
Short Answer Type:
4 Marks (3 out of 5) & Long Answer Type: 12 Marks (4 out of 6)
Frobenius Method and Special Functions:
Frobenius method and its applications to differential equations. Legendre, Bessel, Hermite and Confluent Hypergeometric Differential Equations. Properties of Legendre Polynomials: Rodrigues Formula, Generating Function, Orthogonality. Simple recurrence relations. Expansion of function in a series of Legendre Polynomials. Bessel Functions of the First Kind: Generating Function, simple recurrence relations. Zeros of Bessel Functions and Orthogonality.
Some Special Integrals:
Beta and Gamma Functions and Relation between them. Expression of Integrals in terms of Gamma Functions. Error Function (Probability Integral).
Partial Differential Equations:
Solutions to partial differential equations, using separation of variables: Laplace's Equation in problems of rectangular and spherical symmetry. Wave equation and its solution for vibrational modes of a stretched string.
Reference Books:
• Mathematical Methods for Physicists: Arfken, Weber, 2005, Harris, Elsevier.
• Fourier Analysis by M.R. Spiegel, 2004, Tata McGraw-Hill.
• Mathematics for Physicists, Susan M. Lea, 2004, Thomson Brooks/Cole.
• Differential Equations, George F. Simmons, 2006, Tata McGraw-Hill.
• Partial Differential Equations for Scientists & Engineers, S.J. Farlow, 1993, Dover Pub.
• Mathematical methods for Scientists & Engineers, D.A. McQuarrie, 2003, Viva Books
PHYSICS LAB- LAB C V (2 Credits) FM: 25
PHYSICS-C VI:ELECROSTATICS AND MAGNETISM
(Credits: Theory-04) Theory: 60 Lectures
Mid Semester: 15 End Semester: 60 Full Marks: 75
Short Answer Type:
4 Marks (3 out of 5) & Long Answer Type: 12 Marks (4 out of 6)
Electric Field and Electric Potential
Electric field:
Electric field lines. Electric flux. Gauss’ Law with applications to charge distributions with
spherical, cylindrical and planar symmetry.
Conservative nature of Electrostatic Field. Electrostatic Potential. Laplace’s and Poisson Equations and
their solutions . The Uniqueness Theorem. Potential and Electric Field due to a dipole. Force and Torque
on a dipole.
Electrostatic energy of system of charges. Conductors in an electrostatic Field. Surface charge and force
on a conductor. Parallel-plate capacitor. Capacitance of an isolated spherical conductor.
Separation of variable:
rectangular Cartesian coordinate, spherical coordinate
Method of images:
point charge close to a grounded conducting plane, point charge near a grounded
conducting sphere;
Multipole expansion ;
Multipole expansion of the electrostatic potential, monopole, dipole, quadrupole
approximations at large distances,
Dielectric Properties of Matter:
Electric Field in matter. Polarization, Polarization Charges. Electrical
Susceptibility and Dielectric Constant. Displacement vector D. Relations between E, P and D. Gauss’ Law
in dielectrics. Claussius-Mossotti equation, Langevin- Debye equation
Magnetic Properties of Matter: Magnetization vector (M). Magnetic Intensity (H). Magnetic
Susceptibility and permeability. Relation between B, H, M. Ferromagnetism. B-H curve and hysteresis.
Boundary conditions at the interface of two media and application to a sphere of magnetic material
placed in a uniform magnetic induction, Damagnetizing factor. Origin of magnetic moment. Langevin’s
theory of Diamagnetism and Paramagnetism.
Reference Books:
• Electricity and Magnetism, Edward M. Purcell, 1986 McGraw-Hill Education
• Introduction to Electrodynamics, D.J. Griffiths, 3rd Edn., 1998, Benjamin Cummings.
• Feynman Lectures Vol.2, R.P.Feynman, R.B.Leighton, M. Sands, 2008, Pearson Education
• Elements of Electromagnetics, M.N.O. Sadiku, 2010, Oxford University Press.
• Electricity and Magnetism, J.H.Fewkes & J.Yarwood. Vol. I, 1991, Oxford Univ. Press.
PHYSICS LAB- LAB C VI (2 Credits) FM: 25
1. Measurement of field strength B and its variation in a solenoid
2. Measurement of susceptibility of paramagnetic solution (Quinck`s Tube Method)
3. To measure the Magnetic susceptibility of Solids.
4. Verification of Curie-Weiss Law for a ferroelectric material.
5. To draw the BH curve of Fe using Solenoid & determine energy loss from Hysteresis.
PHYSICS-C VII: WAVE AND ACOUSTICS
(Credits: Theory-04) Theory: 60 Lectures
Mid Semester: 15 End Semester: 60 Full Marks: 75
Short Answer Type:
4 Marks (3 out of 5) & Long Answer Type: 12 Marks (4 out of 6)
Fourier Series:
Periodic functions. Orthogonality of sine and cosine functions, Expansion of
periodic functions in a series of sine and cosine functions and determination of Fourier
coefficients. Complex representation of Fourier series. Even and odd functions and their Fourier
expansions. Application. Analysis of saw-tooth and square wave.
Oscillations:
Simple Harmonic Oscillations. Differential equation of SHM and its solution.
Kinetic energy, potential energy, total energy and their time-average values. Damped oscillation.
Forced oscillations: Transient and steady states; Resonance, sharpness of resonance;
Wave Motion:
Plane and Spherical Waves. Longitudinal and Transverse Waves. Plane
Progressive (Travelling) Waves. Wave Equation. Particle and Wave Velocities. Differential
Equation. Pressure of a Longitudinal Wave. Energy Transport. Intensity of Wave.
Velocity of Waves:
Velocity of Transverse Vibrations of Stretched Strings. Velocity of
Longitudinal Waves in a Fluid in a Pipe. Newton’s Formula for Velocity of Sound. Laplace’s
Correction.
Acoustics:
The acoustics of halls, Reverberation period, Sabine's formula. Acoustic defects in a hall
and their correction.
Reference Books
• Waves and Acoustics, P. K. Chakraborty and Satyabrata Chowdhury.
• The Physics of Vibrations and Waves, H. J. Pain, 2013, John Wiley and Sons.
• The Physics of Waves and Oscillations, N.K. Bajaj, 1998, Tata McGraw Hill.
• Waves: Berkeley Physics Course, vol. 3, Francis Crawford, 2007, Tata McGraw-Hill.
PHYSICS LAB- LAB C VII (2 Credits) FM: 25
1. Verification of laws of transverse vibration in a string using sonometer.
2. Determination of speed of sound using Kundt’s tube.
3. To determine the frequency of electrically maintained tuning fork by Melde’s
experiment.
4. To determine the Density of material of wire using sonometer.
5. To determine the Velocity of sound by resonance column.
Next :: SEMESTER IV
