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ECE 329
Homework 1
Due: June 18, 2009, 5PM
1.
Review exercises on vectors:
Consider the 3D vectors
A
= 3ˆ
x
+ˆ
y

2ˆ
z,
B
=ˆ
x
y

ˆ
C
x

y
+ 3ˆ
where
ˆ
x
≡
(1
,
0
,
0)
,
ˆ
y
≡
(0
,
1
,
0)
, and
ˆ
z
≡
(0
,
0
,
1)
constitute an orthogonal set of unit vectors directed
along the principal axes of a righthanded Cartesian coordinate system.
Vectors can also be represented in component form — e.g.,
A
= (3
,
1
,

2)
, which is equivalent to
3ˆ
x
y

z
.
Determine:
a) The vector
D
≡
A
+
B
,
b) The vector
A
+
B

4
C
,
c) The vector
magnitude

A
+
B

4
C

.
d) The unit vector
ˆ
u
along vector
A
+2
B

C
.
e) The
dot product
A
·
B
.
f) The
cross product
B
×
C
.
2. A particle with charge
q
=1
C passing through the origin
r
=(
x, y, z
) = 0
of the lab frame is
observed to accelerate with forces
F
1
= 3ˆ
F
2
F
3
= 3ˆ
z
+ 4ˆ
y
N
when the velocity of the particle is
v
1
=0
,
v
2
= 1ˆ
y,
v
3
= 2ˆ
z
m
s
,
in turns. Use the Lorentz force equation
F
=
q
(
E
+
v
×
B
)
to determine the Felds
E
and
B
at the
origin.
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 Fall '08
 Kim
 Electromagnet

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