Q 1 [3 marks]
A sphere with a uniform volume charge density 0 and radius R has its centre at the origin
of the spherical coordinate system (r, , ). Consider a section of this sphere between = /3
and = /2 surfaces, as shown in the figure.
of the electric
PH 103 : Eletriity and Magnetism
Mutlipole Expansion and Dieletris
Tutorial Sheet 6 :
Multipole Expansion
1. An eletri dipole
p~
the eletri ux through the hemispherial surfae
and entred at the origin. [Ans.:
2. A dipole
p~ = p k
with the z -axis. Calulat
EP-307
ASSIGNMENT-1
Solutions
Quantum Mechanics II
27th July 2017
Problem-1:
Orbital angular momentum of electron is `. So total angular momentum is
` + 21 to` 12 . For ` = 2, total angular momentum is 25 and 32 . CG matrix of
these values are given below
Expt-5
Helmholtz Coils
Aim
a)
b)
To measure the magnetic field produced by the Helmholtz coil.
To determine the torque experienced by a current carrying loop,
suspended between the Helmholtz coils, as a function of:
(i) the strength of the magnetic moment
Expt-1
Diffraction of Light
Aim
To observe the intensity patterns generated by the diffraction of a laser
beam when passed through a single slit, a double slit and a pin-hole and
to measure the sizes of these diffracting elements up to micro-meter
(micron
What is Fusion Arc Welding?
Definition
Fusion arc welding involves joining of two or more metals together by
localized heating and melting using an electric arc. On solidification, a
joint is formed.
Types of Fusion Arc Welding
Shielded Metal Arc Welding
Examples of using Schrdinger
equation: Elementary problems in
Quantum Mechanics
Normalization
h
ih
=
+ V
2
t
2m x
2
2
1. If is a solution A is also one.
2. The total probability of finding the particle
in the region should be one. This in onedimension gi
Problem
A copper wire of cross-sectional area
3.3x 10-6 m2 is carrying a current of 25
A. One meter length of this wire has a
resistance of 5.8x 10-3 ohms. Calculate
the conductivity, drift velocity of the
electrons, electron mobility and mean
free path o
Concepts in Materials Science I
Quantum Statistical Mechanics Primer
VBS/MRC
Quantum StatMech 0
Concepts in Materials Science I
Why Quantum StatMech?
Nature is really quantum mechanical.classical
statmech is an approximation (and typically a good
one at h
PH-107 (2013)
Tutorial Sheet 7
(Wave Mechanics)
* Problems to be done in tutorial.
P1: A particle of mass m is under the influence of a potential
, where x is the displacement from origin and is a
1
V m 2 x 2
2
constant. The ground state wave function of
PH-107 (2013)
Tutorial Sheet 5
(de Broglie Wavelengh, Uncertainty Principle)
* Problems to be done in tutorial.
P1*: Show that the Bohrs condition of quantization of angular
momentum leads to a condition of formation of standing wave of
electron along the
PH-107 (2013)
Tutorial Sheet 3 (Lorentz and Velocity
Transformation)
* Problems to be done in tutorial.
P.1: An observer in frame S sees a pulse of light emitted from its
origin at t=0. The pulse moves in its x-y plane making an angle of
( ) with x-axis.
Additional problems for Special Relativity
August 24, 2013
1. Causality and Relativity: Consider two inertial frames moving with
respect to each other (v < c) in a one dimensional Euclidean space.
Show that causality is not violated if an upper speed limi
Massachusetts Institute of Technology
Physics Department
Physics 8.20
Special Relativity
IAP 2005
January 28, 2005
FINAL EXAM
Instructions
You have 2.5 hours for this test. Papers will be picked up promptly at 5pm.
The exam is scored on a basis of 100
Study Questions on Special Relativity
I.
Short answer questions: Notediagrams are finedont hesitate to use one to
illustrate your point!
1.
What is an invariant? Give an example of an invariant in special relativity.
2.
Explain how Einsteins assumption th
PH-107 (2013)
Tutorial Sheet 8
(Quantum Statistics and Free Electron Theory)
P1: In how many ways three electrons can occupy ten states (the
states include spin degeneracy)? Is the number same as the way
in which three persons can occupy ten chairs in a r
15112013
Semiconductors
Were considered special, because
their conductivity increases with
temperature.
Si, Ge, Indirect gap semiconductors.
Si:6 CB, Ge:8 half CB
Indirect gap for Si 1.1 eV, Ge,0.72 eV.
Electrons in CB per Unit Volume
n
ct
g( )f ( )
PH-107 (2013)
Tutorial Sheet 2 (Lorentz Transformation)
* Problems to be done in tutorial.
P.1*: (a) The length of a rod in a frame in which is at rest (proper
length) is . What would be its length in a frame which moves with
a speed v relative to the rod
PH-107 (2013)
Tutorial Sheet 9
(Band Theory)
P1: (a) The wave function of the free electron can be written as
(x) Aeikx . Use the momentum operator to show that px k .
(b) The wave function of an electron subjected to a periodic force
in a one-dimensional
PH 108 : Electricity and Magnetism
Tutorial Sheet 2 :
Coloumb's law, Gauss's law and Potential
1. A semi-innite slab of thickness t has a uniform charge density distributed in its
volume. Find the electric eld intensity at a distance z from the median pla
Vector calculus
Vector calculus
slope
Gradient (vector)
For a scalar func,on = (x),
For = (x,y,z),
length element
Vector operator DEL
GRADIENT of scalar func,on which is a vector
where is the
PH 108 : Electricity and Magnetism
Tutorial Sheet 4 : Conductors
1. Three identical parallel metallic plates are kept with separation a and b between the
first and second and the second and third plates, respectively. A charge +Q is placed
on the central
Calculating potentials :
Multipole Expansion
Multipole Expansion
P
d
r
where
d
O
Volume
Multipole Expansion
2
1
3
(1) Monopole term
Potential due to charge at the origin
exact potential
Higher multipole terms vanish
(2) dipole term : If Qtot = 0, then
PH 108: Electricity and Magnetism
Tutorial Sheet 3 : Multipoles and Solution to Lapalces
equation
Multipole expansion
1. An electric dipole p~ is fixed at the origin, making an angle with the z-axis. Calculate
the electric flux through the hemispherical s
PH 108 : Electricity and Magnetism
Tutorial Sheet 5 : Dielectrics
1. A uniformly polarized dielectric sphere of radius R has a frozen-in polarization P~ = P0 k.
Calculate the bound surface ( b ) and volume (b ) charge densities. Calculate the electric
fie
PH 108: Electricity and Magnetism
Tutorial Sheet 1 : Coordinate system
and vector calculus
1. For a circle given by the equation, r = 2R cos , where R is the radius of the circle and
(r, ) are the polar coordinates, calculate the following:
(a) area of th
PH 108 : Electricity and Magnetism
Tutorial Sheet 6 : Magnetostatics
~ = K0 (i + j). Calculate the rate
1. A surface current density in the x-y plane is given by K
of flow of charges across a straight line joining the points A(2,0) with B(2,2) in the plan
PH 108 : Electricity and Magnetism
Tutorial Sheet : Faradays law and displacement current
1. A rectangular metalic wire of mass m, width w, length L and resistance R falls through a
~ = B0i in a specified region under the influence of gravity as shown in