HW1 Solution
PHYS 436 HW11
May 1, 2012
Pro. 12.34
Problem
1
For particles with the same mass, the Classical energy is
1
E = mv 2
2
The relative velocity between them is
vrel = v
x
( v) x = 2v
x
which implies the relative energy is
1 2
1
= m (2v)2 = 4E
Ere
PHYS 436 HW1 Solution
Chun Kit Chan
February 14, 2012
Pro 8.3 The setting of the hemisphere for this problem is given in Fig. 1
Figure 1: Setting of coordinates of the problem (Fig. 8.4 of Griths)
From E.X. 5.11 of Griths, we have the vector potential as
PHYS 436 HW6 Solution
by Chun Kit Chan
March 8, 2012
Pro. 9.26 1
Problem
(a) Eqn. 9.179 is only true when the E and B-field have the form of Eqn. 9.176. Then
@B
@t
@
@
@
@
)
x +
y + z E0 (x, y)ei(kz !t) =
B0 ei(kz !t)
@x
@y
@z
@t
ikEy ) + y (ikEx @x Ez )
PHYS 436 HW9 Solution
April 9, 2012
Problem
Pro. 11.111
(a) For a perfect electric dipole at the origin, Eqn 11.12 and Eqn 11.17 of Griths give
p0 cos
!
r
sin ! t
40 r
c
c
0 p0 !
r
A(r, , t) =
sin ! t
4r
c
V (r, , t) =
+
1
cos ! t
r
r
c
where is me
PHYS 436 HW11
HW10 Solution
April 23, 2012
Pro. 12.181
Problem
(a) From Griths Eqn. 12.12, we have
t
x
y
z
=
=
=
=
t
x
y
z
vt
Thus, with
0 1
ct
B C
= B x C
X
@ y A
z
we can write
0
with
Text
and
1
0
1
0
0
B
= B
X
@ 0
0
= v/c
0 1
ct
BxC
C
X=B
@yA
z
0
0
1
Problem 1
(a) From the translational and rotational symmetry about z - axis, the vector potential A is
a function of s and t only. Thus (using the symbol R = r r0 and A (r, t) = A (s, t) here.)
0
A (s, t) = z
4
Now the current can be written as
1
1
I (tr
PHYS 436 HW2 Solution
Chun Kit Chan
February 14, 2012
Pro. 8.71
Problem
The setting of the solenoid of this problem is given in Fig. 1
Figure 1: Setting of coordinates and parameters of the problem (Fig. 8.7 of Griths)
We let Is (s) be the current on the
PHYS 436 HW4 Solution
by Chun Kit Chan
February 22, 2012
Problem
1
Pro. 9.16
Here x-z plane is the plane of incidence, I , R and T are the angle of incidence,
reflection and transmission respectively and z is the normal of the boundary surface. The fields
PHYS 436 HW Solution
by Chun Kit Chan
March 2, 2012
Most of the values for the resistivity, conductivity and permittivity are taken from the wikipedia
and is taken to be approximately 0 . We should recognize that as those quantities vary a lot,
what is re
PHYS 436 HW3 Solution
Chun Kit Chan
February 14, 2012
Pro. 9.7 1
Problem
(a) For a line segment
Then,
z with deformation f (z), the forces acting on it are
2
@ f
Frestoring = T 2
z
@z
@f
Fdissipation = Fdrag =
z
@t
@ 2f
Frestoring + Fdissipation = Ftot
PHYS 436 HW8 Solution
April 3, 2012
Pro. 11.11
Problem
Eqn. 11.12 says
V (r, , t) =
p0 cos
40 r
!
sin ! t
c
r
c
+
1
cos ! t
r
r
c
Eqn. 11.17 says
A(r, , t) =
0 p 0 !
sin ! t
4r
r
c
z
Thus,
@V
p0 cos
=
@t
40 r
!
cos ! t
c
r
c
1
sin ! t
r
r
c
an
PHYS 436 HW 7Solution
by Chun Kit Chan
March 12, 2012
Pro. 10.3 1
Problem
@A
rV
@t
@
1 qt
r
=
@t
40 r2
1 q
r
=
40 r2
E =
B = r A
1
1 @Ar 1
@Ar
=
+
r sin @
r
@
= 0
= 0 r E
r
q
=
r
4
r2
= q (r)
1
J =
0
rB
@E
0
@t
=0
Since B is continuous everywhere, th
Lecture 3
Examples and Problems
Mechanics & thermodynamics
Equipartition
First Law of Thermodynamics
Ideal gases
Isothermal and adiabatic processes
Reading: Elements Ch. 1-3
Lecture 3, p 1
William Thomson (1824 1907)
a.k.a. Lord Kelvin
First wrote down Se
Lecture 2: Ideal Gases
FRIDAY:
Lecture in 190 ESB
Today:
Kinetic Theory
Equipartition (many student ?s)
First Law of Thermodynamics
Internal energy
Heat
Keep up with prelectures, HWs, etc.
using byteshelf / website calendar
increasing T
Pressure
Office
Lecture 4:
Classical Illustrations of Macroscopic Thermal Effects
Heat capacity of solids & liquids
Thermal conductivity
References for this Lecture:
Elements Ch 3,4A-C
Reference for Lecture 5:
Elements Ch 5
Lecture 4, p 1
Q
C
T
Last time: Heat capacity
Physics 213
Ask the Professor Lecture #1
Do you have any questions from last lecture, general comments (polite criticism
always welcome), or good jokes? Just tell us which lecture you attend, and we'll try to
respond appropriately.
Can we have kitten and
Lecture 7
Entropy and Exchange between Systems
Counting microstates of combined systems
Volume exchange between systems
Definition of Entropy and its role in equilibrium
Reference for this Lecture:
Elements Ch 6
Reference for Lecture 8:
Elements Ch 7
L
Lecture 6
Statistical Processes
Irreversibility
Counting and Probability
Microstates and Macrostates
The Meaning of Equilibrium
(m)
9 spins
-9
-7
-5
-3
-1
1
3
5
m
7
9
Lecture 6, p. 1
Irreversibility
Have you ever seen this happen?
(when you werent asl
Lecture 11
Applying Boltzmann Statistics
Elasticity of a Polymer
Heat capacities
CV of molecules for real !
When equipartition fails
Reading for this Lecture:
Elements Ch 8
Reading for Lecture 12:
Elements Ch 9
Lecture 11, p 1
Last time: Boltzmann
Distr
Lecture 8
The Second Law of Thermodynamics;
Energy Exchange
The second law of thermodynamics
Statistics of energy exchange
General definition of temperature
Why heat flows from hot to cold
Reading for this Lecture:
Elements Ch 7
Reading for Lecture 10
Lecture 9
Examples and Problems
Counting microstates of combined systems
Volume exchange between systems
Definition of Entropy and its role in equilibrium
The second law of thermodynamics
Statistics of energy exchange
General definition of temperatu
Lecture 5:
Diffusion
Thermal Diffusion
Random Walk and Particle Diffusion
Reading: Elements Ch. 5
Lecture 5, p 1
Heat Conduction Summary
Heat current density J is the heat flow per unit area through a material.
Units: Watts/m2
J = - dT/dx
(- sign becaus
Lecture 10
The Boltzmann Distribution
Concept of a thermal reservoir
The Boltzmann distribution
Paramagnetic Spins MRI
Reading for this Lecture:
Elements Ch 8
Reading for Lecture 11:
Elements Ch 9
Lecture 10, p 1
Some Questions
Wed Like to Answer
What is
PHYS 436 Homework 2 CHECKPOINT SHOW YOUR WORK!
#1) In the absence of surface current, the perpendicular component of S is continuous.
qB0 c 2
S
(0, 0, sin )
=
#2) a)
(in spherical coordinates)
4 r 2
S =0
b) There is no net flow of energy
0
L=
L=
x
y
c)
PHYS 436 Homework 1 CHECKPOINT SHOW YOUR WORK!
#1) a) W =
Q2d
2 0 A
Q2d
b) W =
2 0 A
#2) a)
= j0 cos x
t
b) Hint: To know if charge is conserved, you must know the total charge in the system.
Physics 436
Homework 6
Due February 27, 2017
1. We saw in lecture that for the radial E, tangential B wave in a coaxial cable the current in
the center conductor (actually, in either conductor) equals the linear charge density times the
speed of light (i.
Physics 436
Homework 9
Due March 27, 2017
1. An electron with initial speed vi c approaches a distant repulsive Coulomb potential
!
Ze2
. The electron will travel in a straight line, decelerating until it stops and
PE(r) = +
4 0r
!
reverses direction. Sho
Physics 436
Due March 6, 2017
Homework 7
1. Recall that the resonant TE modes in a rectangular box are mnl = c
( ) +( ) +( )
m
a
2
n
b
2
l
d
2
1
2 ,
where a, b, and d are the box dimensions. There are similar TM modes in the box.
a. Calculate the approxi
Physics 436
Homework 2
Due January 30, 2017
Note: Problem 3 is worth 10 points.
1. Recall the boundary conditions on static E and B at an interface between two materials:
E !and!B are always continuous, and H! is continuous in the absence of free surface
Physics 436
Homework 4
Due February 13, 2017
1. Injection of light into an optical fiber.
source:&
shell:&ns#
Light from a source enters the end of a cylindrical fiber with
ni#
incident angle , as shown. The source has an index of
core:&nc#
i#
refraction