Chapter 1: Introduction to Electromagnetics and Electromagnetic
Fields
1.1
Review of foundations
1.1.1
Introduction
Electromagnetics involves the macroscopic behavior of electric charges in vacuum and matter.
This behavior can be accurately characterized
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
2
6.013 Electromagnetics and Applications
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Student Name:
4
Final Exam
Closed book, no calculators
May 18, 2009
Please note the two pages of formulas provide
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications Quiz 2 Solutions
Problem 1. (28/100 points)
a) Th = 100 ohms since there is no glitch at t = 2 and therefore no refle
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Quiz 1 Solutions
Problem 1. (34/100 points)
a)
E = 2 x cos(t + z) andH = y sin(t z ) .
2
z
(t z) 0 velocity v
1 [m/s]
Solutions to Problem Set 12
12.1 (a) c = sin-1(k2/k1) = sin-1(c1/c2) = sin-1(2/1)0.5 = 80.9 degrees
(b) x = (kz2-ko2)0.5 where kz/ko = sin 850. It follows that -1 = 0.60 o
(c) D = ~4o. Note that decay is rapid relative to D, so we might guess D = ~0
Problem Set 11 Solutions
Problem 11.0
The easiest way to approach this problem is to pretend that the roof antennas are transmitting to an antenna
at the horizon. Then for each antenna orientation, we can nd the image antenna and the distance from the
roo
Problem Set 9 Solutions
Problem 9.1
(a)
The waveguide will propagate only one mode in the frequency range between the two lowest cuto frequencies.
The cuto frequency for the T E10 (which is the mode with the lowest cuto frequency) is:
c2
f10 =
= 12.5 10
Problem Set 7 Solutions
Problem 7.1
(a)
(i) For an air lled line we know that the propagation velocity is c . Looking at the gure we see the
distance between adjacent voltage minima is A, so the wavelength is = 2A. The frequency of the wave is
given by th
6.1
Problem 6.1
GIVEN
Innitely-long stripline for which d = 1 m and the medium between the plates has = 0
and = 40 .
6.1.1
FIND
Width, W , for which the characteristic impedance of the line is 50 . Discuss whether ideal
parallel plate model is valid for t
Problem Set 5 Solutions
Problem 5.1
(a)
(i) For a quarter wave plate we know that the dierence in phase gained from propagating through the plate
between the component polarized along the fast axis and the component polarized along the slow axis is
/2. W
4.1
Problem 1
GIVEN:
A circular-cross-section pill magnet of diameter D produces a nearly uniform
magnetic eld, B0 , across its broad face. We wish to estimate B0 using two
dierent methods: induced voltage and force measurement.
4.1.1
Part a
FIND:
If the
Problem Set 3 Solutions
Problem 3.1
(a) Using the force/energy equation, we know that the force attracting the two plates will be equal to the
partial derivative of the stored energy in the system with respect to the changing variable (in this case, d).
f
W
,
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t
tKZ<
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&/E
tKZ<
/t
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D
tKZ< d
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HW2 Page 1
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t
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2.2
Problem 2
GIVEN
If the electric eld is E (t) =
E (t) if
Eejt , where E is a phasor, then what is
FIND
(a) E = 1 j
WORK
ejt = cos(t) + j sin(t) by Eulers the