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: __________________
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Problem 1. A closed loop ( x  30cm  y  20cm ) of wire passes through a nonuniform
time-independent magnetic field B  yaz T with a constant velocity v0=5ax
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.
y
v(t)
y
B
x
x
Answer:
Problem 2. A conducting axle oscillates over two conducting parallel rails in a uniform
magnetic field B=B0a z (B0=4 T). The position of the axle is given by
x  (x / 2)[1  cos t ] ( x  0.2m ,   500s 1 ). Find and plot the current I(t)
if the resistance is R=10  and the distance between the rails is y  0.1m
y
I
R
B
y
x
x
Answer:
Problem 3.
The time harmonic electric fields inside a source-free perfect magnetic
conducting (PMC) rectangular waveguide are given by

H  H 0 sin( y )e  jkz z a x , 0  x  a, 0  y  b
b
Assume that the media inside the waveguide is free space, and four side walls at
x  0, a and y  0, b are perfect magnetic conductor. For a section of the
waveguide of length l along z axis from z  0 to z  l , find:
(1) time domain expression of electric fields;
(2) k z ;
Answer:
Problem 4. An electromagnetic wave with a frequency f=1MHz propagates in a dielectric
material (  r  4, r  1 ) and has an electric field component
E y ( z, t )  1.3cos(t  kz ) V/m . Find the velocity of the wave, the wave
vector k, the characteristic impedance of the material Zc, 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 ay -az)exp(j4x) 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 3 10 8 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 r  1 and  r  2.5 ). The wavelength
in free space is 0  30 cm.
Answer:
Problem 7. Find the skin depth  at a frequency 4MHz in aluminum, where
  3.82  107 S/m and  r  r  1 , Also find the phase velocity v p .
Answer: