Update5/12/08
Physics
633, Electricity and Magnetism 2
Lectures
M,W,F 9:30, CW 023
Instructor:
C.L.Cocke, 532-1609, cocke@phys.ksu.edu,
www.phys.ksu.edu/personal/cocke
Office
hours: MWF,
Text: Introduction to Electrodynamics, David
Griffiths, Third Edition, Prentice Hall
Problems 4 due Feb. 25: Problem 9.21,9.23 (a),9.25 ; plus
1) A conducting material can be heated by induction heating
by exposing it to a time varying magnetic field. Suppose a good conductor (with
skin depth delta) is exposed to a magnetic field which has a component
tangential to the surface given by B=Bo exp (-iwt).
The surface lies in the xy plane, and B is in the y
direction.
a) Using the
boundary conditions on B, find B(z,t) inside the material.
b) This B will cause an electromagnetic wave to propagate
into the material. Using the form of this wave developed in class,
calculate the Poynting vector into the surface,
evaluated just at the surface.
c) Using the value of E for this wave, and j=sigma*E, find
the surface current flowing in the conductor. By integrating over z, find the
current per unit length flowing in the surface of the conductor (this extends
roughly over the skin depth of the conductor). Make a clear sketch to show that
you understand the geometry and which way the surface current flows.
d) Using the boundary condition on tangential B which applies
if there is a surface current (extending over a thickness of several skin
depths), show that the current found in (c) is just enough to kill the incident
B.
e) Calculate the ohmic heating in
the surface by integrating j dot E over the volume of the material, and show
that it agrees with the answer to (b).
f) Calculate the numerical value of the skin depth for Cu at
60 Hz. How large a piece of Cu would you expect to be able to heat this way?
2) An electromagnetic wave at 1 kHz is sent OUT of sea water
(conductivity 5/ohm-m) in normal incidence into air.
a) Show that sea
water is a good conductor at this frequency and find the skin depth.
b) Write the form of the incident, reflected and transmitted
waves. Assume the wave is sent in the positive z direction and is polarized in
the x direction. Describe the nature of each wave: damped, traveling, etc.
c) Find the ratio of the strength of the electric field of
the incident wave just below the surface to that of the transmitted wave just
above the surface, to first order in the skin depth.
d) What fraction of the power reaching the surface is
transmitted through the surface?
****
Problems 5 due
1) For the coaxial cable discussed in class, show that the surface
currents and surface charges on the inner conductor, derived from the
expressions for E and B in the cable, satisfy charge conservation.
****
Problems 6 due
***
Problems 7 due
1) A charge q moves at
omega around a circle of radius A in the xy plane. Do
the following for an arbitrary point x (on the x axis, y=z=0) and z (on the z
axis, x=y=0). Assume that x and z are very much larger than A
and that the velocity of the charge is very much less than the speed of
light. Using the expression that E is the retarded transverse acceleration divided
by R (times some constants),
a) Find E at both locations. Show that your answer agrees
with your answer to problem 10.20.
b) Find S.
c) Find the total power radiated by the charge. (Hint: you can consider the charge as
executing two independent oscillations, one along x and one along y and just
add the powers).
d) Use this expression to calculate the expected lifetime of
an electron in the first Bohr orbit of a Hydrogen atom.
2) When a charged particle (of mass m and velocity v) passes
rapidly by the nucleus of an atom, it feels a force which accelerates it and
thus causes it to radiate. To calculate the power radiated requires finding the
resulting electric field E
and integrating S over the time it takes to pass, and over the
angular distribution of the radiation. This is messy, but a good estimate can
be made using the following approximations: 1) That the acceleration is
constant and approximately that which the particle feels at its closest
distance (b) to the nucleus;(2) That the duration of
the “pulse” of radiation is 2b/v, where v is the velocity of the particle.
Assume that v travels in a nearly straight line. Using this model, and assuming
the observer is far from the nucleus, and v is non-relativistic,
a) Find E as a function of theta, where theta is the angle
between the acceleration vector and the observation point.
b) Find S at this point.
c) Integrate S over the angle and over the pulse duration to
find the total energy radiated.
d) At what distance b would a 20 keV
electron have to pass to a Cu nucleus (Z=29) to radiate an energy equal to 1
percent of its total energy?
***********
Problems 8 due
1. For the case of a M1 radiator,
a) Work out E and B from the expression for A given in class.
b) Work out the total power radiated.
c) Show that the ratio of the total power radiated by an M1
radiator to that of an E1 radiator carrying the same peak current and of the
same physical size (d of E1 oscillator equal to a of M1 oscillator) is given by
(kd)^2
(eq. 11.42). Which radiator is
likely to be more efficient in practical cases?
2. Consider two antennae. One is a magnetic dipole made of a
single loop 10 cm in diameter, and the other is an electric dipole 10 cm long.
Answer each of the following questions for 10 khz and for 100 Mhz:
a) Radiators: What rms current is
required for each antenna to radiate 1 kwatt?
b) Receivers: What rms voltage will
be developed in each in the presence of an electromagnetic wave in air carrying
a power of one milliwatt per square meter? (optimize the alignment of each antenna).
******
Problems due
Do not forget to retake the quiz (unless you were perfect
first time) as a take home, and turn it in April 14.
*****
Problems, due April 30. 2008: 12.17,12.20,12.25, 12.32, 12.33
****
Problems, due May 7, 2008:
12.44, 12.47, 12.23
Problem set solutions:
PS1 and 2, PS 3 and 4, PS 5 and 6 ,PS 7, PS 8; Quiz 2 prime; PS rest
Lecture notes
Schedule (subject to change):
Date Subject Chapter
Jan.
18 Maxwell’s equations 7.3
Jan.
28 Conservation laws 8
Feb.
4 Electromagnetic Waves 9
Mar.
7 Potentials and Fields 10
Mar.
31 Radiation 11
Apr.
28 Relativity 12
Exams
will be given on Feb. 29 and April 7. Short quizzes will be given from time to
time.
The
final exam will be given on May 16,
Homework: Homework assignments will
be made each week. The due date will be stated on each assignment. THE HOMEWORK
MUST BE TURNED IN ON THE DATE DUE TO RECEIVE CREDIT. Late assignments will not be
accepted except in special circumstances approved in advance by the instructor.
The homework is to be written clearly on one side of the paper. You MUST
explain what you are doing in order to receive any credit for the problem. A
page full of scribbled equations is not acceptable. You are encouraged to work
together to understand the problems, but you must turn in your own work.
Remember also that on the exams you will be working alone.
Exams
and quizzes:
The quizzes will be open book. Calculators and math tables will be allowed.
The
final grade
will be based on the course work as shown below:
Homework
50%
Exams
and quizzes 30%
Final
exam 20%
University
policy requires that the following be placed on this syllabus:
I. Disabilities: If you have any condition
such as a physical or learning disability, which will make it
difficult
for you to carry out the work as I have outlined it or which will require
academic accommodations, please notify me and contact the Disabled Students
Office (Holton 202), in the first two weeks of the course.
II.
Plagiarism: Plagiarism and cheating are serious offenses and may be
punished by failure on the exam, paper or project; failure in the course;
and/or expulsion from the University. For
more information refer to the "Academic Dishonesty" policy in K-State
Undergraduate Catalog and the Undergraduate Honor System Policy on the