EEL 3470 Electromagnetic Fields

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16 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

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Department

of Electrical
Engineering and Computer Science


EEL 3470 Electromagnetic Fields


Homework Set No. 5


Please turn in your answers, MatLab files and results.

Each group
should turn in ONLY one set of homework.

Print this page and write your answers. After that, attach your MatLab files and results.


Names: __________________ ___________________ ___________________



Problem 1
.
A closed loop (
30cm 20cm
x y
   
) of wire passes through a nonuniform
time
-
independent magnetic field
y

z
B a
T with a constant velocity
=5
0 x
v a

m/s. At t=0, the loop

s lower left corner is located at the origin. Find an
expression for the voltage V, generated by the loop as a function of time.
You may neglect the magnetic field created by the current in the loop.

B
y
x
v
(
t
)


Answer:


x


y


Problem
2
.
A conducting axle oscillates over two conducting parallel rails in a uniform
magnetic field
0
=
z
B
B a
(
B
0
=4 T). The
position

of the axle is given by
(/2)[1 cos ]
x x t

  

(
0.2m
x
 
,
1
500s




). Find and plot the current
I
(
t
)

if the resistance is R=10


and the distance between the rails is
0.1m
y
 

B
I
y
R
x



Answer:



Problem
3
.



The time harmonic electric fields inside a source
-
free perfect magnetic


conducting (PMC) rectangular waveguide are given by


b
y
a
x
e
y
b
H
x
z
jk
z






0

,
0

,
)
sin(
0
a
H




Assume that the media inside the waveguide is free space, and four side walls at
a
x
,
0

and
b
y
,
0


are perfect magnetic conductor. For a section of the


waveguide of length
l
along z axis from
0

z

to
l
z

, find:

(1)

time domain

expression of electric fields;

(2)

z
k
;

x


y



Answer:



Problem 4
.
An electromagnetic wave with a frequency f=1MHz propagates in a dielectric
material (
4,1
r r
 
 
) and has an electric
field

component
y
E (,) 1.3cos( ) V/m
z t t kz

 
. Find the velocity of the wave
,

the wave
vector
k
, the characteristic impedance of the
material

Z
c
, and the magnetic
field
H
(
z,t
).



Answer:



Problem 5
.


The phasor

form expression for the electric field of a uniform plane wave

propagating in lossless isotropic medium is



E
(
x
) = 60

2

a
y
-
a
z
)
exp(j4
x
) V/m.

The magnetic field at point (0,0,0) when t = 0 is
2
A/m. The unit of t is

second and the unit of
x

is meter. The radian frequency is
8
10
3


rad/s. Find

(1)


the time domain expression of the electric field;

(2)


the wave impedance

of the media;

(3)


the relative dielectric constant

r
and relative permeability

r;

(4)


the time domain expression for magnetic field;



Answer:



Problem 6
.
Find the attenuation constant


(Np/m), the phase constant


(rad/m) and
the phase velocity
v


if the conductivity


of the material is such that
 


(the material parameters are
1
r



and
2.5
r


). The
wavelength

in free space is
0
30


cm.


Answer:



Problem 7
.

Find the skin depth


at a frequency 4MHz in aluminum, where
7
3.82 10 S/m

 

and
1
r r
 
 
, Also find the phase velocity
p
v

.


Answer: