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ECE 329
Exam 1 review
Fall 2008
TIME: Sept. 25, 2008, 7  8:15 pm
LOCATION: Section X: CA 112 — Chemistry Annex
(Other sections in SIEBEL 140)
You will be allowed to bring
one
8
1
2
×
11
inch sheet of notes (both sides) to the exam.
Calculators are not allowed.
Chapter 1
•
All electric and magnetic phenomena in nature can be attributed to the existence of electrical charge
and charged particle motions.
In classical descriptions, charge carriers having charge
q
and mass
m
are treated as
“point particles"
(or “test charges") which obey Newton’s 2nd law of motion
(
F
=
m d
v
/dt
).
In the presence of an electric ﬁeld
E
and magnetic ﬁeld
B
(which are related to
distant charge carriers as described by Maxwell’s equations), such a point particle will not aFect the
ﬁelds in its vicinity, yet it will experience a force
F
(and thus an acceleration) as it moves with a
velocity
v
through the ﬁelds as described by the
Lorentz force law
:
F
=
q
(
E
+
v
×
B
)
.
•
Here,
F
,
E
,
B
and
v
are all vector ﬁelds which can be expressed in Cartesian coordinates in terms of
mutually orthogonal unit vectors
ˆ
x
,
ˆ
y
and
ˆ
z
. Principle of superposition. Dot product. Cross product.
Right hand rule
.
•
Charge carriers generate
E
.
The
E
generated by a
stationary point charge
having charge of
Q
[C] is radially symmetric around
Q
and decreases inversely as the square of the distance from the
charge (
Coulomb’s Law:
E
=
Q/
(4
π±
0
r
2
)
ˆ
r
[V/m]), where
±
0
is the
permittivity of free space
.
The electric ﬁeld due to a positive charge
Q
is directed radially outward, while that of a negative
charge is directed inward. The
E
ﬁeld arising from a distribution of multiple stationary point charges
or extended line, surface, or volume charges can be found using Coulomb’s Law in superposition for
each source (or diFerential charge element).
±or symmetric charge distributions, using Gauss’ Law
for
E
is often a more e²cient approach for ﬁnding
E
(see Ch. 2 below). Either approach yields the
following:
–
An inﬁnite charge distribution of uniform density
ρ
L
[C/m] along the
ˆ
z
axis produces
E
at a
distance
r
[m] given by
E
=
ρ
L
/
(2
π±
0
r
)
ˆ
r
[V/m].
–
An inﬁnite surface charge distribution of uniform density
ρ
S
[C/m
2
] produces
E
given by
E
=
ρ
S
/
(2
±
0
)
ˆn
[V/m], in the direction normal to the sheet.
•
A moving charge carrier (i.e.,
current
) generates
B
. The (inﬁnitesimal) magnetic ﬁeld generated at
a radius
r
by an inﬁnitesimal current element
I
dl
is along the direction
I
dl
×
ˆ
r
and is given by the
BiotSavart Law:
dB
= (
μ
0
/
4
πr
2
)(
I
dl
×
ˆ
r
)
[Wb/m
2
], where
μ
0
is the
permeability of free space
.
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 Spring '08
 Kim

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