MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
Problem Set No. 2
6.630 Electromagnetic Theory
Issued:
Week 2
Fall Term 2006
Due:
Week 3
                                                                             
Reading assignment
: Section 1.31.4; J. A. Kong, “
Electromagnetic Wave Theory
,” EMW,
2005.
Problem P2.1
Prove the following identities:
∇ ×
∇ ×
E
=
∇
∇
·
E
 ∇
2
E
∇
·
E
×
H
=
H
·
∇ ×
E

E
·
∇ ×
H
∇
·
∇ ×
A
= 0
∇ ×
(
∇
φ
) = 0
Problem P2.2
Consider an electromagnetic wave propagating in the ˆ
z
direction with
E
= ˆ
xe
x
cos(
kz

ω
t
+
ψ
x
) + ˆ
ye
y
cos(
kz

ω
t
+
ψ
y
)
where
e
x
,
e
y
,
ψ
x
, and
ψ
y
are all real numbers.
(a) Let
e
x
= 2
, e
y
= 1
,
ψ
x
=
π
/
2
,
ψ
y
=
π
/
4
.
What is the polarization?
(b) Let
e
x
= 1
, e
y
=
ψ
x
= 0
.
This is a linearly polarized wave. Prove that it can be
expressed as the superposition of a righthand circularly polarized wave and a left
hand circularly polarized wave.
(c) Let
e
x
= 1
,
ψ
x
=
π
/
4
,
ψ
y
=

π
/
4
, e
y
= 1
.
This is a circularly polarized wave. Prove
that it can be decomposed into two linearly polarized waves.
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 Spring '09
 Zahn
 Computer Science, Electron, Light, Electromagnet, Fundamental physics concepts, Massachusetts Institute of Technology Department of Electrical Engineering

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