Multipole expansions
The potential due to a point charge is given by a simple q expression : V(r) = 40 | r rq | Suppose the charges are distributed over a localized region, then 1 (r' ) 3 the potential is given by V(r) = 4 | r r' | d r ' , which could 0
Boundary values problems in electrostatics
The uniqueness theorem If we specified the potentials at all the boundaries (i.e. surfaces) of a charge-free region of space, and want to know the potentials at every points in the region, we have a boundary valu
Ch.3
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 3
Ordinary Differential Equations
An ordinary differential equation is an equation containing ordinary (not partial) derivatives of the unknown function. The order of an ordin
Chapter 2 Review of statistical mechanics
13
14
CHAPTER 2. REVIEW OF STATISTICAL MECHANICS
2.1 Principles of statistical mechanics
2.1.1 Macroscopic and microscopic states
A macroscopic system is made of a huge number of particles. The power of thermodyna
Ch.2
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 2
Some Applications of Calculus
2.1 Maxima and Minima of Functions
2.1.1 Stationary Points
A point at which the derivative of a function f x vanishes,
f x0 0 .
(2.1.1)
A stati
Electricity and Magnetism
Overview
All matters possess a property called charge, interactions between charges give rise to almost all the phenomena we experienced in our daily life (except for the effects from gravity). Anything you can think of, e.g. co
PHYS 5510: Advanced Statistical Physics
Ren-Bao Liu Department of Physics, The Chinese University of Hong Kong rbliu@cuhk.edu.hk 2010-2011, 1st Term c Copyright reserved. No reproduction or redistribution of any part is allowed without written permission
Ch.1
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 1
Vector Algebra, Coordinate Systems and Related Topics
1.1 Vector Algebra
1.1.1 Scalars and Vectors
Scalars: quantities require only a real number to represent their size (or
Ch.3
PHYS2041 Problems in Quantitative Methods for Basic Physics (1st Term 10/11)
Chapter 3
Techniques of Integration
3.1 Method of Substitution
One may make the integration of a function simpler by using substitution of variable. To illustrate the method
Ch.2
PHYS2041 Problems in Quantitative Methods for Basic Physics (1st Term 10/11)
Chapter 2
Differential and Integration
2.1 Concepts of Limit and Continuity
2.1.1 Definition of Limit:
A function F, which is defined on the domain x1 x c and c x x2 ,
is sa
PHYS2004 (1st Term 10/11)
Assignment 4
Section A (Compulsory due on 21/10/2010 Thu (before 5:00 pm) 1.
The curvature of a curve traced out by the position vector r t is defined as
dr d 2 r 2 dt dt 3 . dr dt
Find , given that (a) (b) r t a sin ti a cos t
PHYS2004 (1st Term 10/11)
Assignment 3
Section A (Compulsory due on 14/10/2010 Thu (before 5:00 pm) 1. A point P moves on the curve
r a exp cot ,
in such a way that its radius vector OP rotates about the origin with the constant
angular velocity . Find t
PHYS2004 (1st Term 10/11)
Assignment 2
Section A (Compulsory due on 30/09/2010 Thu (before 5:00 pm) 1. Show that the four points: A 1, 1, 0 , B 2, 0, 1 , C 2, 1, 2 and D 4, 4, 1 coplanar and find the equation of the plane containing them. [50 marks] 2. Fi
PHYS2004 (1st Term 10/11)
Assignment 1
Section A (Compulsory due on 22/09/2010 Wed (before 5:00 pm ) 1.
(a) Given that a i k and b 3i 2 4k , find (i) the projection vector of j j a in the direction of b , and (ii) the projection vector of b in the direct
Ch.1
PHYS 2041 Problems in Quantitative Methods for Basic Physics (1st Term 10/11)
Chapter 1
Elementary Numbers
Functions
and
Complex
1.1 Exponential and Logarithmic Functions
The exponential function of x is denoted as e x or exp x and the inverse functi
PHY2822 Exp.5 Prelab ex Balmer series of H Electron transition: from n = 4 to n = 2. Wavelength = 486.1 nm Energy E = h =
hc
=
1240 eV nm = 2.551 eV 486.1 nm
PHY2822 Exp. 4 Prelab ex. 2:
R R B ( x ) =k [ R 2 + ( x ) 2 ]3/ 2 + [ R 2 + ( x + ) 2 ]3/ 2 x 2 2 NIR 2 where k 0 . 2
R R 3( x ) 3( x + ) dB( x ) 2 2 =k + R R dx [ R 2 + ( x ) 2 ]5 / 2 [ R 2 + ( x + ) 2 ]5 / 2 2 2
R 2 5/ 2 R2 2 R 2 3/ 2 2 [ R + ( x 2 ) ]
Maximally ecient quantum thermal machines: The basic principles
Sandu Popescu
H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom (Dated: September 15, 2010) Following the result by Skrzypczyk et al., ar
THE CHINESE UNIVERSITY OF HONG KONG Department of Physics Second Term, 2009-2010 PHY 0222 Physics Problems II
Date Topic Group Time Room
REVISED 8.01.10
Jan 13
Jan 20
Jan 27
Feb 3
Feb 10
Feb 24
Mar 3
Mar 10
Mar 17
Mar 24
Mar 31
Apr 7
A B C D E F G H I J K
2009-2010 2nd Term PHY0222 Physics Problems II Problem Set 1 (Thermodynamics 1) Physics 2002 STOT
1 . O ne inole of iu1.y gas at room temperature ;and a tlllosphe~ic ressure (10"ynes/cln2) p is found experimentally to occupy a v olu~ne f approxinlately 24
PHY 0222 STOT Problem Set E3 (March 17, 2010)
1. A conical surface (empty ice-cream cone) carries a uniform surface charge density . The height of the cone and the radius at the top are both equal to a (Fig. 1). Find the potential difference between the v
PHY 0222 STOT Problem Set E1 (January 27, 2010)
1. Some point charges, each of charge +q, are distributed at the corners of a regular star-shaped polygon as shown in Fig. 1. In particular, the two charges on the y axis are located at (0, a) and (0, -b), w
PHYS 4260 Statistical Mechanics [Week 1, 6-10 September 2010] (Sample Question SQ1)
There WILL BE exercise classes on 8 Sept (Wednesday) 2010 and 9 Sept (Thursday) 2010 in Week 1 of classes. The TA will do the SAME THING in the two sessions. You SHOULD ma
Chapter 7 Phase Transition III: Landau Theory
7.1 Order parameter
In Landau theory of phase transition, a phase transition is signaled by the emergence of a thermodynamic quantity, which is zero above the transition temperature and grows (or jumps) to be
Electrodynamics
In electrostatics and magnetostatics, both the E-field and Bfield are time-independent. They are relevant to cases where we have a fixed charge distribution and steady current Faraday discovered that a changing magnetic flux through a cir
Chapter 6 Phase transition II: Ising model (A)
In this chapter we discuss the phase transition of Ising model, using the mean-eld approximation. The Ising models partition function can be exactly calculated in one- and two-dimensional lattices. It provide
Magnetic fields in matter
All matters contain magnetic moments, either from the orbital motion of a charge particle (e.g. electron in an atom) or from the intrinsic properties of an elementary particle the spin There are three major kinds of magnetic res
Chapter 5 Phase Transition I: van der Waals Gas
5.1 General remarks
Phase transitions occur at discontinuities of the equilibrium thermodynamic functions with varying certain physical parameters such as temperature, density, magnetic eld, etc. For a nite
Ch.5
PHYS2004 Quantitative Methods for Basic Physics I (1st Term 10/11)
Chapter 5
Transcendental Functions
5.1 Transcendental Functions
By definition, y f x is an algebraic function of x if it is a function that satisfies an irreducible algebraic equation