EE 4301.002.15S Engineering Electromagnetics I: Assignment #5
Problems due Thursday, March 12th at the beginning of class no late assignments will be
accepted.
Problem 1: Consider the dielectric materials configured in the figure. The interface between
th
EE4301 Electromagnetic Engineering I
Assignment 1
Exercises are from the textbook
Elements of Engineering Electromagnetics, Sixth
Edition, by Nannapaneni Narayana Rao (Pearson Education, 2004); ISBN 0131139614
Exercise 1
Re-do step by step the example pre
Exercises
811
controls the overall transport rate. Thus, changes in that resistance have a larger
overall effect on the total transport.
Section 14.3
14.13 Consider Eq. (14.41), which is used to describe an axon subjected to a membrane
potential. Assume a
Exercises
807
V (mV)
100
0
I (mA/cm2)
100
0
1
2
4
6
8
Na
K
L
C
0
1
0
1
2
4
6
8
10
n
m
h
0.5
0
0
0.4
10
2
4
6
8
10
n4
0.2
0
0
m3h
2
4
6
8
10
Time (ms)
Figure 14.18 HodgkinHuxley action potential. Upper pane shows the membrane
voltage resulting from the sti
808 Chapter 14
Biological Systems: Transport of Heat, Mass, and Electric Charge
source (Q2), the energy removed by the perfusion term (Q3), and the energy leaving
the tumor by conduction (Q4). These quantities are defined as follows:
Rt
Q1 = 4pS
3
r2dr =
Exercises
809
For the acid titration, that is, when we are adding H + , we use Eq. (14.11) and
express the proton concentration as [H + ] = [H + ]i + y where [H + ]i is the initial proton
concentration and y is the amount of acid added, usually HCl, which
Section 14.3
Charge Transport in Biological Systems
805
Eq. (14.41), the equation requiring that the sum of the membrane currents be
zero is given by
dV
-1
=
C i + iNa + iL D
dt
Cm K
(14.42)
-1
=
C g A V - EK B + gNa A V - ENa B + gL A V - EL B D
Cm K
whe
810 Chapter 14
Biological Systems: Transport of Heat, Mass, and Electric Charge
where Pe is a constant and 0CT,O2>0CO2 is given by Eq. (14.29). For the parameters
appearing in Eq. (14.29), use those given in Example 14.7. It will be found that the ability
Section 9.4
Free and Forced Vibrations
501
TABLE 9.3 Nomenclature for Timoshenko Beam Formulation: Dimensional Quantities
Quantity
Units
General
x
w(x, t) = W(h)Le jvt
L
r
A
E
G = E/(2(1 + n)
n
v
I
ro = 2I / A
to = 3 A rAL B >(EI)
4
mb = rAL
c(x,t) = (h)e
Section 9.4
Free and Forced Vibrations
503
Using Eqs. (9.60) and (9.61) in Eq. (9.58), we obtain
dy2(h)
= y4(h) - gbs R2 A 4 + 4Md(h - hm) - Kd(h - hk) B y1(h)
o
dh
dy4(h)
=
dh
(9.62)
A -y2(h) + y3(h) B ^ A gbs R2 B - A R2 4 + J 4d(h - hm) - Ktd(h - ht) B
504
Chapter 9
Dynamics and Vibrations
Then, Eqs. (9.61a) and (9.62) form a set of four first-order equations that can
be used by bvp4c to find a numerical solution. The boundary conditions given by
Eq. (9.63) are also in a form that can be used by bvp4c.
Section 9.4
Free and Forced Vibrations
505
The program is implemented assuming a cantilever beam with the following
parameters: M = 0, J = 0, K = 100 at ht = 0.5, Kt = 0, MR = 0.3, JR = 0.1, KR = 100,
and KtR = 5. For these parameters, we assume that gbs
506
Chapter 9
Dynamics and Vibrations
disp(['Boundary conditions: Left end - ' BCL ' Right end - ' BCR])
disp(' ')
if isempty(find(b> 0, 1) = 0
disp('Attachments at right end - ')
disp(['Translation spring (KR) = ' num2str(b(3) ' Torsion spring (KtR) = '
508
Chapter 9
Dynamics and Vibrations
switch BCL
case 'clamped'
bc = [y0(1); y0(4)-0.05; y0(3)];
case 'hinged'
bc = [y0(1); y0(2)-0.05; y0(4)];
case 'free'
bc = [(y0(2)-y0(3); y0(1)-0.02; y0(4)];
end
switch BCR
case 'clamped'
bc = [bc; y1(1); y1(3);];
cas
806 Chapter 14
Biological Systems: Transport of Heat, Mass, and Electric Charge
rectangular pulse of current density equal to 0.2 mA/cm2, which starts at 2 ms and lasts
for 0.1 ms. This depolarization trigger causes the ion channels to open slightly, whic
804 Chapter 14
Biological Systems: Transport of Heat, Mass, and Electric Charge
plot(t, y(:,1), 'k-', t, c, 'k-')
legend(gate(k), L, 'Location', 'East')
if k = 3
xlabel('t (ms)')
end
end
function dy = HH(t, y, g)
V = -65+65*(t>2)&(t<5);
dy = alph(V+65, g)
EE4301 Electromagnetic Engineering I
Assignment 12
Exercise 1 Problem P 6.7
The system shown in Figure 1 is in steady state.
40
Z0 75
100V
T 1 s
60
z l
z0
Figure 1
Find
a) The line voltage and current
b) the (+) wave voltage and current
c) the (-) wave
2. The current densities of two infinite, plane, parallel current sheets are given by:
=
cos
=
cos
, = 0
,
=
2
< 0; ! 0 <
Find the electric-field intensities in the three regions:
Solution:
First we find the electric-field due to the first curre
118. Why is it not necessary
magnetic ux density de-
Vhat are its units?
iow do you determine the
: sheet of uniform surface
to charge distributions and
:e on a moving charge?
on a current-carrying wire
m the knowledge of forces
velocities. What is the mi
EE 4301.501 Engineering Electromagnetics I: Assignment #2
Problems due Tuesday, September 17th at the beginning of class no late
assignments will be accepted.
Problems in text beginning on page 72: P1.29, P1.
EE 4301.501 Engineering Electromagnetics I: Assignment #5
Problems due Tuesday, October 22th at the beginning of class no late assignments will be
accepted.
Problem 1: The capacitor shown has a capacitance given by
where is the dielectric
constant of the
EE 4301.501 Engineering Electromagnetics I: Assignment #3
Problems due Tuesday, September 24th at the beginning of class no late assignments will be
accepted.
Problem 1: Three identical point charges of 4C each are located at the corners of an
equilateral
EE4301.501 Engineering Electromagnetics I: Assignment #7
Problems are due Tuesday December 10th at the beginning of class no late assignments will be
accepted. In this assignment, the bold faced expressions represent vectors.
Problem 1: The following char
EE 4301.001.17S
Assignment #8
Spring 2017
This assignment is due on Tuesday, April 31th at the beginning of class no late
assignments will be accepted.
Problem 1: In the circuit shown, the resistance of the left rail is fixed and equal to
R1 . The top and
EE4301.501 Exam#2 Solutions
Problem 1: Skin depth is given for a plane wave propagating in graphite
50:8.854-1012- '1: 5,: 12.7 ez=erceo
7 H
0:24.10 .E I-l'r:=1 p:=lJ,r-p,a
f:=100-MHz w:=2-1r-f 6:=0.16omm
a) Assuming that graphite is a good conductor at
EE 4301.501 Engineering Electromagnetics I: Assignment #4
Problems due Tuesday, October 15th at the beginning of class no late assignments will be
accepted.
Problem 1: The circuit shown is situated in a magnetic field with time varying flux density given
EE4301.501
Exam #1
Fall 2013
Problem 1 (25 points):
a) For
parallel to the sum
b) For
(
)
and
and
find a unit vector
.
(
) find a unit vector perpendicular to both
at the point
. Express
your answer in Cartesian coordinates.
c) A surface is given by t