BSc Physics Notes: Semester 2

Semester 2

 

List of the Subjects 


CORE: ELECTRICITY AND MAGNETISM


CORE: WAVES  AND OPTICS


GE: LINEAR ALGEBRA 




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PHYSICS-C III: ELECTRICITY AND MAGNETISM (Credits: Theory-04, Practicals-02)       
Theory:  60 Lectures 

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Topics Covered in Notes

 

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. 
                                                           (6  Lectures) 


Conservative  nature  of  Electrostatic  Field.  Electrostatic  Potential.  Laplace’s  and  Poisson equations.  The  Uniqueness  Theorem.  Potential  and  Electric  Field  of  a  dipole.  Force  and Torque on a  dipole.        
                                                           (6 Lectures) 


Electrostatic  energy  of  system  of  charges.  Electrostatic  energy  of  a  charged  sphere. Conductors  in  an  electrostatic  Field.  Surface  charge  and  force  on  a  conductor. Capacitance  of  a  system  of  charged  conductors.  Parallel-plate  capacitor.  Capacitance  of an  isolated  conductor.  Method  of  Images  and  its  application  to:  (1)  Plane  Infinite  Sheet and (2) Sphere.       
                                                          (10 Lectures) 


Dielectric  Properties  of  Matter:  Electric  Field  in  matter.  Polarization,  Polarization Charges.    Electrical  Susceptibility  and  Dielectric  Constant.  Capacitor  (parallel  plate, spherical,  cylindrical)  filled  with  dielectric.  Displacement  vector  D.  Relations  between E,  P  and  D.  Gauss’ Law in dielectrics.     
                                                           (8 Lectures) 


Magnetic    Field:  Magnetic  force  between  current  elements  and  definition  of  Magnetic FieldB.  Biot-Savart’s  Law  and  its  simple  applications:  straight  wire  and  circular  loop. Current  Loop  as  a  Magnetic  Dipole  and  its  Dipole  Moment  (Analogy  with  Electric Dipole) Ampere’s  Circuital  Law  and  its  application  to  (1)  Solenoid  and  (2)  Toroid.  Properties  of  B:  curl  and  divergence.  Vector  Potential.  Magnetic  Force  on  (1)  point charge  (2)  current  carrying  wire  (3)  between  current  elements.  Torque  on  a  current  loop in a uniform Magnetic Field.      
                                                            (9 Lectures) 


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.    
                                                          (4 Lectures) 


Electromagnetic  Induction:  Faraday’s  Law.  Lenz’s  Law.  Self  Inductance  and  Mutual Inductance.  Reciprocity  Theorem. Energy stored in a Magnetic  Field.  Introduction  to Maxwell’s Equations. Charge Conservation and  Displacement current. 
                                                          (6 Lectures) 


Electrical  Circuits:  AC  Circuits:  Kirchhoff’s  laws  for AC circuits.Complex Reactance and  Impedance . Series  LCR  Circuit:  (1)  Resonance,  (2)  Power  Dissipation  and  (3) Quality  Factor, and (4) Band Width. Parallel LCR Circuit.       
                                                           (5  Lectures) 


Network  theorems:  Ideal  constant-voltage  and  constant-current  Sources.  Review  of Kirchhoff’s Current  Law  &  Kirchhoff’s Voltage  Law.  Mesh  &  Node  Analysis.  Thevenin theorem,  Norton  theorem,  Superposition  theorem,  Reciprocity  Theorem,  Maximum Power Transfer  theorem.  Applications to dc circuits.     
                                                           (6  Lectures) 






Suggested Books in Syllabus: 
  • Electricity,  Magnetism  &  Electromagnetic  Theory,  S.Mahajan  and  Choudhury, 2012, Tata McGraw 
  • 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 
  • Electricity  and Magnetism, J.H.Fewkes  &  J.Yarwood. Vol.I, 1991, Oxford Univ. Press. 






Click to download the Notes in Pdf Format

Handwritten 





                
                                                                                                                                                




DU  Vle






References:

  • Class Notes 
  • Electricity and Magnetism by D C Tyal
  • DU  Vle  Notes
  • Introduction to Electrodynamics by Griffith's.








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 PHYSICS-C IV:   WAVES  AND OPTICS 
(Credits: Theory-04,  Practicals-02)       
Theory:  60 Lectures 

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               Topics Covered in Notes


Superposition  of  Collinear  Harmonic  oscillations:  Simple  harmonic  motion  (SHM). Linearity  and  Superposition  Principle.  Superposition  of  two  collinear  oscillations  having (1) equal  frequencies  and  (2)  different  frequencies  (Beats). Super-position  of  N  collinear Harmonic  Oscillations  with  (1)  equal  phase  differences  and  (2)  equal  frequency differences.           
                                                            (6  Lectures)


Superposition  of  two  perpendicular  Harmonic  Oscillations: Graphical and Analytical Methods.  Lissajous Figures  with equal and unequal frequencies  and their uses.
                                                              (2 Lectures) 


Wave  Motion:  Plane  and  Spherical  Waves.  Longitudinal  and  Transverse  Waves.  Plane Progressive  (Travelling)  Waves.  Wave  Equation.  Particle  and  Wave  Velocities. Pressure of a Longitudinal Wave. Energy  Transport.  Intensity  of Wave.   
                                                             (4 Lectures) 


Superposition  of  Two  Harmonic  Waves:  Standing  (Stationary)  Waves  in  a  String: Fixed  and  Free  Ends.  Analytical  Treatment.  Phase  and  Group  Velocities.  Changes  with respect  to  Position  and  Time.  Energy  of  Vibrating  String.  Transfer  of  Energy.  Normal Modes  of  Stretched  Strings.  Longitudinal  Standing  Waves  and  Normal  Modes . Open and Closed Pipes.  Superposition of N Harmonic Waves.    
                                                              (8  Lectures)


Wave  Optics:  Electromagnetic  nature  of  light.  Definition  and  properties  of  wave  front. Huygens Principle. Temporal and Spatial Coherence.   
                                                              (4  Lectures) 


Interference:  Division  of  amplitude  and  wave-front.  Young’s  double  slit  experiment. Lloyd’s  Mirror  and  Fresnel’s  Biprism.  Phase  change  on  reflection:  Stokes’  treatment. Interference in  Thin  Films:  parallel  and wedge-shaped  films.  Fringes  of  equal  inclination (Haidinger  Fringes);  Fringes  of  equal  thickness  (Fizeau  Fringes).  Newton’s  Rings: Measurement of wavelength and refractive index.   
                                                             (10  Lectures) 


Interferometer:  Michelson  Interferometer-(1)  Idea  of  form  of  fringes  (No  theory required),  (2)  Determination  of  Wavelength,  (3)  Wavelength  Difference,  (4)  Refractive Index, and (5) Visibility  of Fringes.  Fabry-Perot interferometer.    
                                                            (6  Lectures) 


Diffraction:   Fraunhofer  diffraction:  Single  slit.  Rectangular  and  Circular  aperture,  Resolving  Power of  a  telescope.  Double  slit.  Multiple  slits.  Diffraction  grating.  Resolving  power  of grating.                                                                  (10  Lectures) 


Fresnel  Diffraction:  Fresnel’s  Assumptions.  Fresnel’s  Half-Period  Zones  for  Plane Wave.  Explanation of Rectilinear Propagation of Light. Theory  of a  Zone Plate: Multiple Foci  of  a  Zone  Plate.  Fresnel’s  Integral,  Cornu`s  spiral  and  its  applications.  Straight edge, a  slit and a wire.                                                                         (10  Lectures) 






Suggested Books in syllabus:
  • Waves: Berkeley  Physics Course, vol. 3,  Francis Crawford, 2007, Tata McGraw-Hill. 
  • Fundamentals of Optics,  F.A. Jenkins and H.E. White, 1981,  McGraw-Hill 
  • Principles of Optics, Max  Born and Emil Wolf, 7th  Edn., 1999,  Pergamon Press. 
  • Optics, Ajoy  Ghatak, 2008, Tata McGraw  Hill 
  • 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. 
  • Fundamental  of  Optics,  A.  Kumar,  H.R.  Gulati  and  D.R.  Khanna,  2011,  R.  Chand Publication









Click to download the Notes in Pdf Format






 





References:

  • Class Notes
  • The Physics of Waves and Oscillations by N K Bajaj.
  • Optics by Ajoy Ghatak. 
  • Optics by Brijlal and Subramanian. 








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GE-2: Linear Algebra 
Total Marks: 100 
Examination: 3 Hrs. 

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Course Objectives: The objective of the course is to introduce the concept of vectors in n. The concepts of linear independence and dependence, rank and linear transformations has been explained through matrices.Various applications vectors in computer graphics and movements in a plane has also been introduced. 


Course Learning Outcomes: This course will enable the students to:  
i) Visualize the spacenin terms of vectors and the interrelation of vectors with matrices.  
ii) Learn about linear transformations, transition matrix and similarity.  


Topics Covered in Notes 



Unit 1: Euclidean space n and Matrices Funda-mental operation with vectors in Euclidean space n, Linear combination of vectors, Dot product and their properties, Cauchy-Schwarz inequality, Triangle inequality, Projection vectors, Some elementary results  on  vectors  in ;n Matrices: Gauss–Jordan row reduction, Reduced row echelon form, Row equivalence, Rank, Linear combination of vectors, Row space, Eigenvalues, Eigenvectors, Eigenspace, Characteristic polynomials, Diagonalization of matrices; Definition and examples of vector space, Some elementary properties of vector spaces, Subspace, Span of a set, a spanning set for an eigenspace, Linear independence and linear dependence of vectors, Basis and dimension of a vector space, Maximal linearly independent sets, Minimal spanning sets; Application of rank: Homogenous and non-homogenous systems of linear equations; Coordinates of a vector in ordered basis, Transition matrix.    
                                                      (Lectures: 35)     

                                                                                              Unit 2:  Linear Transformations and Computer Graphics , Linear transformations: Definition and examples, Elementary properties, The matrix of a linear transformation, Linear operator and similarity; Application: Computer graphics, Fundamental movements in a plane, Homogenous coordinates, Composition of movements; Kernel and range of a linear transformation, Dimension theorem, One to one and onto linear transformations, Invertible linear transformations, Isomorphism, Isomorphic vector spaces (to n).  
                                                      (Lectures: 25)


Unit 3:  Orthogonality and Least Square Solutions      Orthogonal and orthonormal vectors, Orthogonal and orthonormal bases, Orthogonal complement, Projection theorem, Orthogonal projection onto a subspace; Application: Least square solutions for inconsistent systems, Non-unique least square solutions. 
                                                       (Lectures: 10)








Suggested Books in Syllabus :  
  • Andrilli, S., & Hecker, D. (2016). Elementary Linear Algebra (5th ed.). Academic Press, Elsevier India Private Limited.
  • Kolman, Bernard, & Hill, David R. (2001). Intro-ductory Linear Algebra with Applications (7th ed.). Pearson Education, Delhi. First Indian Reprint 2003. 







Click to download the Notes in Pdf Format












References:

  • Class Notes
  • Elementary Linear Algebra by Andrilli
  • Mathematical Physics by H K Das








with regards,

By Bsc Physics Notes

Vaibhav Tyagi
Personal Homepage : Click Here
PhD in Atmospheric Sciences
Indian Institute of Technology Indore, MP
M.Sc. Physics (2020-2022)
Indian Institute of Technology
Palakkad , Kerala 

B.Sc. Honours Physics (2017-2020)
Deen Dyal Upadhyaya College
University of Delhi

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