**
ECE 520.219-220, Fields, Matter, and Waves, Fall'09
<br>
<h2>
<a href="http://striky.ece.jhu.edu/~sasha/COURSES/EM.descript.09.pdf">
ECE 520.219-220, Fields, Matter, and Waves
</a>
</h2>
<br>
taught by
<a href="http://psi.ece.jhu.edu/~kaplan/">
Prof. Alexander Kaplan </a>, Barton Hall, #304, alexander.kaplan@jhu.edu
<br>
at
<a href="http://www.ece.jhu.edu/">
Elect. & Computer Eng. Dept.</a>
of <a href="http://www.jhu.edu/home.html"> JHU </a> <br>
<p>
<br>
The class is held on Mondays & Wednesdays, in
Barton Hall, #117, 3:00-4:15. First meeting -- Sept. 2'09
<br>
Class assistant: Beibei Zhang, Barton Hall, #404, z_man_bj@hotmail.com
<br>
Office hours: Alex Kaplan, Mondays, 1:00--3:00 pm
<br>
Beibei Zhang, Wed. 12-2
<br>
<br>
Home work #1
<br>
Problems:
<br>
1.1, 1.5, 1.7, 1.9 (a,b), 1.13, 1.19, 1.25
<br>
<a href="hw1.pdf">
see PDF-file with all the above problems
</a>
<br>
<br>
Home work #2
<br>
Problems:
<br>
2.2, 2.6, 2.8, 2.14, 2.21, 2.25
<br>
plus the problem of field vs distance R from
a center of sphere with the total charge Q and radius R_0.
<br>
<br>
<a href="solut.Hw2.PDF">
see PDF-file with the solutions
of all the above problems (including
the one with a charged sphere)
</a>
<br>
<br>
Home work #3
<br>
Problems:
<br>
3.4, 3.10, 3.12, 3,14, 3.20, 4.4, 4.8, 4.12, 4,16
<br>
<a href="solut.Hw3.pdf">
see PDF-file with the solutions of the above problems
</a>
<br>
<br>
Home work #4
<br>
Problems:
<br>
4.22, 4.28, 4.30, 5.4, 5.6, 5.10
<br>
plus two other problems:
<br>
<br>
4.A:
<br>
There are two parallel strings charged with
the linear charge density rho_L and -rho_L
spaced by the distance d, forming a linear dipole.
Find electrical field at the distance R from
the center line of the system in the plane normal
to the strings, in a far-field area (R >> d)
<br>
<br>
4.B:
<br>
An unmoving electron is positioned at a very large
distance R away from a proton, and them set out free.
Attracted by a positively charged proton,
it started to move. Evaluate its velocity
in terms of velocity of light in free space,
when it reaches the point of 0.5 angstrem from the proton.
Assume that proton has an infinite mass.
<br>
<br>
<a href="solut.Hw4.PDF">
see PDF-file with the solutions
of all the above problems (including 4.A and 4.B).
</a>
<br>
<br>
Home work #5
<br>
Problems:
<br>
5.12, 5.16, 5.18, 5. 20, 5.22
<br>
plus two other problems:
<br>
<br>
5.A:
<br>
There is a sphere of radius R_0, filled with initially
unmoving electrons in free space, such that the total
charge is -Q.
The sphere begins blowing apart due to mutual repulsion of
electrons, resulting in a Coulomb explosion.
Find out the dynamics of this explosion,
i.e. how the sphere radius, R, changes in time.
<br>
<br>
5.B:
<br>
An electron is placed above the metall surface
at the distance R.
Find out the distribution of surface
charges at the metall surface
as the function of the distance r from
the point of projection of the electon
onto the surface.
<br>
<br>
<a href="solut.Hw5.pdf">
see PDF-file with the solutions
of the above problems
</a>
<br>
<br>
Home work #6
<br>
Problems:
<br>
5.24, 5.26, 6.1, 6.2, 6.6, 6.8, 6.10, 6.12
<br>
plus one more problem:
<br>
<br>
6.A. A postive charge q is placed in free space in
the middle between two ideally conducting infinite metallic
surfaces spaced by the distance d.
Find the field at any point in the middle
between the surfaces at the distance R_0 from the charge.
<br>
<br>
<a href="solut.Hw6.pdf">
see PDF-file with the solutions
of all the above problems
</a>
<br>
<br>
Home work #7
<br>
Problems:
<br>
6.14, 6.16, 6.17, 6.19, 6.23, 6.24
<br>
plus one more problem:
<br>
<br>
7.A. Find the capacitance of the planet Earth in terms of faradas.
Assume the Earth an ideally conducting sphere.
<br>
<br>
<a href="solut.Hw7.pdf">
see PDF-file with the solutions
of all the above problems
</a>
<br>
<br>
Home work #8
<br>
Problems:
<br>
7.2, 7.3, 7.4, 7.7, 7.17, 7.28
<br>
plus couple more problems:
<br>
<br>
8.A. Write a Laplas-like 1D-equation for the
potential V, if the dielectric constant of a
material is changing in the x-axis as epsilon=1+(x/a)^2,
where "a" is some characteristic length.
Try to solve it for the potential V.
<br>
<br>
8.B. Derive eqns (7.20) and (7.21) in a book;
also check out the eqn preceeding (7.17).
<br>
<br>
<a href="solut.Hw8.pdf">
see PDF-file with the solutions
of all the above problems
</a>
<br>
<br>
Home work #9
<br>
Problems:
<br>
7.19, 7.20
<br>
plus 3 more problems:
<br>
<br>
9.A. For the solution, eq. (7.39), considered in the book
find the family of equipotential surfaces, for which
only one term in (7.39) would suffice. (You may need to look
carefully through the Chapter 7!)
<br>
<br>
9.B. Two wedges in free space (2D-case) with a common axis and
each having wedge angle 2*phi, almost touch each other. Find
spatial diostribution of potential (and equipotential surfaces)
and field distribution in the space around them. The same
question about two conuses with the same conical angle.
(The same instruction as in previous problem.)
<br>
<br>
9.C. An infinite string with the velocity "v" of wave propagation
was deformed in the beginning to form a equal-sided triangular
on its shape, and then let go. What waves would propagate in it after
that? find their exact solution of the problem.
<br>
<br>
<a href="solut.Hw9.pdf">
see PDF-file with the solutions
of all the above problems
</a>
<br>
<br>
Home work #10
<br>
Problems:
<br>
8.2, 8.4(a)(with extra, see below), 8.6, 8.10, 8.12, 8.13, 8.22
<br>
plus 2 more problems:
<br>
<br>
Extra to 8.4(a)of a book: find field H at any point in the z-axis; examine how it attunuates as |z|->infinity.
<br>
<br>
10.A. Prove eq (8.31) in the book by using the defenition of
both NABLA operators in terms of partial derivatives.
<br>
<br>
<a href="solut.Hw10.pdf">
see PDF-file with the solutions
of all the above problems
</a>
<br>
<br>
<a href="project.topics.09.pdf">
Suggested topics for the course project/presentation
</a>
<br>
<br>
Take-Home Final Exam
<br>
Problems:
<br>
2.22, 3.6, 4.18, 7.8, 8.5
<br>
plus 2 more problems:
<br>
<br>
F.A. Two metallic plates parallel to each other, spaced by "d"
and positioned vertically, are immersed into a liquid with the dielectric
constant eps_r > 1, above which there is a free air.
The plates are charged oppositely, with the charge on one
of them being Q. What happened with the liquid between them?
Will it be pushed up or down? and how far?
What happened to the liquid if
instead of charging the plates with a fixed charge
you connect them to a battery with a fixed voltage "V"?
<br>
You may use the relationship for the energy of field (4.46)
or of the capacitor, (6.28).
<br>
<br>
F.B. Two ideally conducting and parallel to each other rails
are immersed in a dc magnetic field "H_0" normal to the
plane of the rails. An ideally conducting wire maintain
a connection between the rails, but is allowed to slide
along them, while staying normal both to the rails and
to the magnetic field. There is a constant current "I"
flowing through one rail to the wire to the another rail.
The magnetic field is turned on at the moment "0".
How far would the wire move under the action of the magnetic
field after time "t"? what would be its speed?
Neglect the magnetic field generated by the current itself.
<br>
<br>
<a href="solutions.FINAL.pdf">
see PDF-file with the solutions
of all the final exam problems
</a>
<br>
<br>
The finals:
<br>
<br>
<a href="FINAL.520.219.2009Fall_anonymous.pdf">
Your anonymous total grades and the finals are posted here
</a>
<br>
<br>
Your graded final exam papers can be found in
a big enevelope attached to the door of my office.
<br>
<br>
If you have any complaints, please email me and I will
look into that; in the end of the week I will turn in
the final grading to Registar.
<br>
<br>
Alex Kaplan
<br>
**