Homepage for PH2101 PHYSICS III
(August-December 2013)
Indian Institute of Science Education and
Research Kolkata
Instructor: Bhavtosh Bansal (bhavtosh)
Teaching Assistants: Anuradha Samajdar (anuradha1115),
Soubhik Kumar (soubhik), Aritra Mukhopadhyay (aritraabir1910)
Lectures: Tuesday 10 am (LH3, Prefab); Wednesday 10 am (LH1,
JCB); Thursday 8 am (LH3, Prefab)
Doubts session: Saturday 11:30 am (LH1, JCB)
Tutorials: Once a week
Summary of Lectures
1. Lecture 1 (Tuesday July
30, 2013): Simple harmonic motion (SHM): The SHM
equation, examples (mass-spring, simple pendulum, compound
pendulum, torsional pendulum, electrical LC circuit, liquid
column). Same differential equation => same solution.
[See examples in French, Chapter 1 and/or Bajaj].
2. Lecture 2 (Wednesday July 31): Solution
of the SHM differential equation (2nd order linear
differential equation with constant coefficients),
determination of unknown constants from initial
conditions, writing the solution in polar form
(amplitude and phase), physical meaning of the
integration constants
3. Lecture 3 (August 2, Friday):
Solution in terms of complex numbers; Why is SHM
so common (Taylor series argument, small displacement
around stable equilibrium gives Hooke's law). Energy in
SHM, calculation of time average values. Damped harmonic
oscillator: Solution of equation of motion. Underdamped,
overdamped and critically
damped systems.
4.
Lecture 4 (August
6, Tuesday):
Phase space trajectory for classical SHM
and damped harmonic motion, phase space
trajectory in quantum mechanics (for
entertainment only). Instantaneous
energy of an oscillator; Q-factor of a
(under-)damped oscillator.
5. Lecture 5 (August
7, Wednesday):
Forced Oscillator. Linear differential
equations and the principle of
superposition. Why choosing a
single-frequency harmonic driving force
is enough to determine the general
behaviour of the system. Transient
and steady state solutions. Elastic and
absorptive amplitudes.
Concept of impedance in mechanical and
electrical circuits.
6. Lecture 6 (August
13, Tuesday):
Power
dissipated and
power absorbed
by a forced
damped
oscillator in
resonance. Amplitude
resonance and velocity resonance. Amplitude
and phase of
the response
as a function
of driving
frequency.
7. Lecture
7 (August
14, Wednesday):
Topics of
lectures 5 and
6 discussed
further.
8. Lecture
8 (August
20, Tuesday):
Damping in forced oscillators. Relationship
between
'full-width at
half maximum'
of the
resonance
curve and
damping
constant.Three
(approximately) equivalent definitions
of the Q factor. Parameteric
oscillations (for 'entertainment' only).
9. Lecture 9 (August
21, Wednesday):
Coupled Oscillations: Two simple
pendula connected by a spring. Normal
modes: Normal coordinates and normal
frequency.
10. Lecture 10 (August
22, Thursday):
Physical
meaning of
normal
coordinates,
expressing
individual
particles'
motion as
superposition
of normal
coordinates.
Examples of
other coupled
systems
(longitudinal
vibrations of
coupled
mass-spring
sytem).
11. Lecture
11 (August
27, Tuesday):
Transverse
vibrations of
mass spring
system.
General method
of finding
normal modes
using the
theory of
coupled linear
equations.
12. Lecture
12 (August
29, Thursday):
Transverse
oscillations
of a beaded
string. General
solution for
normal mode
frequencies
and normal
coordinates.
Solution for
1, 2 and N
masses.
13. Lecture
13 (September
3, Tuesday):
Transverse
oscillations
of a beaded
string
(cont.): Proof
that only N
distinct
normal mode
frequencies
exist, concept
of the wave
number,
Brillouin zone
14. Lecture
14 (September
4, Wednesday):
Continuum
limit of the
expression for
displacement
and normal
mode
frequencies,
transverse
vibrations of
a stretched
string.
15. Lecture
15 (September
5, Thursday):
Transverse
vibrations of
a stretched
string:
Solving the
initial value
problem using
the Fourier
method for
non-zero
velocity and
displacement.
16. Lecture
16 (September
10, Tuesday):
Forced
vibrations of
a stretched
string.
17. Lecture
17
(September 11,
Wednesday):
The continuum
limit. 1D wave
equation.
Travelling
waves.
D'Alembert's
solution.
Harmonic waves
in one
dimension.
Various ways
of writing the
harmonic
solution in
terms of wave
vectors and
angular
frequency,
velocity,
displacement,
and
wavelength,
etc.
18. Lecture
18
(September 12,
Thursday):
Physical
visualization
of waves.
19. Lecture
19 (September
17, Tuesday):
Superposition
of harmonic
waves of two
frequencies,
group
velocity,
phase velocity
and dispersion
relations. Amplitude
modulated
waves and
their use in
radio
communication;
20.
Lecture
20 (September
18,
Wednesday):
Wave packets,
superposition
of harmonic
oscillations
of many
frequencies,
the sinc
function,
bandwidth
theorem,
spread of a
wave packet as
it travels
within a
dispersive
medium.
relationship
between wave
number and
size of wave
packet (\Delta
k). (\Delta
x).
Relationship
with the
quantum
mechanical
uncertainty
relations.
21. Class Test 1 September
19, Thursday
_____________________________________________________________________
Mid
Semester Exam (September 23, Monday): LH3 2pm-3pm (Prefab)
Syllabus:
Everything up to Lecture 16, September
10.
_____________________________________________________________________
22. Lecture 21
(October
01, Tuesday): Electromagnetism:
Maxwell Equations in integral form.
Lorentz force equation. Physical meaning of electric and
magnetic fields, Maxwell equations in differential form. The
continuity equation. Wave equation from Maxwell
equations.
October 2, Wednesday: Holiday: Gandhi Jayanti.
23. Lecture
22 (October 3,
Thursday):
Physical meaning of the wave equation for E and B fields.
Six wave equations. Speed of light in vacuum. The
electromagnetic spectrum. Electromagnetic plane waves E(z,t);
B(z,t). Transverse nature of electromagnetic waves.
Relationship between E and B fields in magnitude, direction
and phase for plane harmonic (single frequency) waves.
Picture of propagating E and B fields. Notion of the wave
vector, k and plane wave propagating along an
arbitrary direction. Relationship between k and
\omega.
24. Lecture 23
(October 4, Friday)
[instead of the class on October 8, Tuesday]: Plane harmonic
electromagnetic waves (cont.). How the original Maxwell
equations simplify when one assumes E(z, t) = E0
cos (kz-wt+\phi) and B(z,t)=B0
cos(kz-wt+\phi). Plane waves and wave fronts.
25. Lecture 24
(October 9,
Wednesday):
Polarization of EM waves. Linear, circular and
elliptical polarization.
26.
Lecture 25
(October
17, Thursday):
Energy density of electric and magnetic
fields, Poynting theorem and Poynting
vector. Poynting theorem for plane harmonic
EM waves. Intensity, momentum and pressure.
27. Lecture
26 (October 22,Tuesday):
Electric fields in
Dielectrics. Qualitative
comments on the Lorentz oscillator model for
a dielectric. Macroscopic (average)
polarization of a dielectric body. Induced
dipole moments in bound charges in external
electric field. Polarization vector P.
Relationship between induced bound surface
charge density and polarization.
28. Lecture
27 (October 23, Wednesday):
Parallel
plate capacitor with
a dielectric slab. Definition
of the dielectric constant. Gauss' law for
dielectrics. Electrical susceptibility,
\chi. D and P vectors.
Modified Maxwell equations in presence of a
dielectric body (and magnetically
polarizable body). [Pl. don't worry about M
and H vectors]
29. Lecture
28 (October 24, Thursday):
Wave
equation inside a
homogeneous
dielectrics.
Refractive
index. Maxwell equations for conductors.
Proof that free charge density cannot exist
within a conductor. Electromagnetic waves in
conductors, dissipation of free charge
density on the surface of a conductor
30. Lecture 29 (October 29,
Tuesday): EM waves in conductors
(cont.). Maxwell equations with Ohm's law.
Derivation of wave-like equation from
Maxwell equations for conductors. Plane wave
solution and complex wave vector. Physical
meaning of complex wave vector and skin
depth. Relative phase and amplitude of
electric and magnetic fields for an EM wave
propagating in conductors.
31. Lecture 30 (October 30,
Wednesday): Microscopic theory for
electrical susceptibility in a dielectric as
a forced damped oscillator.
32. Lecture 31 (October 31,
Thursday): Derivation of the
expression for susceptibility and the
dielectric constant. Meaning and consequence
of the dielectric constant and
susceptibility becoming complex. Absorption
coefficient. Frequency dependence of the
real and the imaginary parts of the
dielectric constant.
33. Lecture 32 (November 05,
Tuesday): Normal and anomalous
dispersion. Cauchy Sellimer relation, phase
velocity and group velocity in the anomalous
dispersion region. How the distinction
between conductors and dielectric blurs at
high frequencies, relation between imaginary
part of dielectric constant and the real
conductivity. Microscopic model of
conductivity (not done in class so can skip
for exam, see pg 441-445 in B&B).
34. Lecture 33 (November 06,
Wednesday): From wave optics to ray
optics. Fermat's Principle- Laws of
reflection and refraction. Focussing
by an ellipse
(qualitative)and by a parabolic mirror.
[In
the class, I followed R Shankar's
lecture: http://oyc.yale.edu/physics/phys-201/lecture-16
. The same topics are also
discussed in Crawford.]
35. Lecture
34 (November 07, Thursday): Interference
of light: Reminder of the expression for intensity of
EM waves. Time and length scales of EM waves corresponding
to visible light. Detectors measure average intensity. Why
it is hard to observe interference of visible light. General
expression for the intensity due to interference of two and
more electric fields. Spherically symmetric solutions of the
wave equation and their physical meaning in terms of
outgoing and incoming waves from and to a point source.
Addition (interference) of spherical waves from two point
sources, phase difference due to path difference. Ideas of
coherence time and coherence length.
36. Lecture 35 (November 12, Tuesday):
Huygen's principle, Young's double-hole interference
formulae for maxima and minima, very qualitative idea of
spatial coherence
37. Lecture 36 (November 13, Wednesday): Generalization
to N equally spaced holes, diffraction grating,
formula for angular variation of intensity,
positions of maxima, use of the diffraction grating
in separating colours
38. Lecture 37 (November 14, Thursday):
Diffraction by a circular hole (only the calculation of
intensity along the axis), Concept of Fresnel (near field)
and Fraunhofer (far field) regions, Babinet's principle and
diffraction by a disc.
39. Lecture 38 (November 19, Tuesday):
Fraunhofer diffraction by a long slit, angular spread of the
diffraction pattern and connection with the bandwidth
theorem.
40. Lecture 39 (November 20, Wednesday): Corrections
to the formulae for double hole and N-hole
interference when the finite size of the
hole is considered. What is actually
observed on the screen. Resolving
power of optical instruments and Rayleigh criterion.
[Resolving power and Rayleigh criterion can be left
out for the exam].
41.
Class Test 2 (November 21, Thursday): 8
am LH 3, Prefab
42. Final Exam November 25, Monday
Suggested References
Vibrations and Waves (You may read any one of them
along with your class notes):
1. Physics of Waves and Oscillations: NK Bajaj (Tata McGraw
Hill)
2. Vibrations and Waves: AP French (CBS Publishers)
3. Waves: Frank S. Crawford Jr. (McGraw
Hill)
4. Physics of Vibrations: HJ Pain (Wiley, 6th Ed)
Electrodynamics
Introduction to Electrodynamics: David J Griffiths (Prentice
Hall India)
Electromagnetic Vibrations, Waves, and Radiation: George Bekefi and
Alan H Barret (MIT Press, 1977)
Interference and Diffraction:
Electromagnetic Vibrations, Waves, and Radiation: George Bekefi and
Alan H Barret (MIT Press, 1977), Chapter 8
Web resources
1. Walter
Lewin's course at MIT is at a similar level as our course.
2.
Richard Fitzpatrick's notes for an Oscillations and Waves course
at University of Texas
3. Applet for wave on a string (http://phet.colorado.edu/en/simulation/wave-on-a-string)
3.
Last Updated: November 19, 2013