ECE 329 Lecture Notes — Fall08, Erhan Kudeki
1 Vector felds and Forces
•
Fundamental building blocks of matter,
electrons
and
protons
, are
elec
trically charged
and exert attractive/repulsive forces upon one another
(depending on algebraic signs of the charges involved) — in general,
all
electric
and
magnetic
phenomena observed in nature can be attributed to
the existence and motions of
electric charge carriers
.
•
In classical descriptions, individual charge carriers (e.g., electrons and pro
tons) are modeled as
point particles
having:
– mass
m
and
charge
q
, conserved and quantized as integer multiples
of proton charge
e
≈
1
.
6
×
10

19
C (coulombs) in all reference frames,
–
well de±ned
locations
r
=(
x,y,z
)
,
–
and trajectories
1
r
=
r
(
t
)
obeying
Newton’s 2nd Law of motion
,
m
¨
r
=
F
,
where
¨
r
≡
d
2
r
dt
2
denotes a particle acceleration and
F
the force applied
on the particle.
•
Electric and magnetic components of
force
F
on a point charge
q
are pro
portional to
q
and expressed in terms of an
electric Feld
E
and
magnetic
Feld
B
produced by distant charge carriers — speci±cally
Lorentz
force
F
=
q
(
E
+
v
×
B
)
,
which is known as
Lorentz force
, where
–
v
≡
˙
r
=
d
r
dt
is the
velocity vector
of charge
q
,
– electric Feld
E
is
by defnition
the vector force per unit charge when
q
is stationary (i.e.,
v
=0
),
Maxwell’s eqns
in diferential
Form (used starting in Chpt 3):
∇·
E
=
ρ
±
o
B
∇×
E
=

∂
B
∂t
B
=
μ
o
J
+
μ
o
±
o
∂
E
with, in MKSA units,
μ
o
≡
4
π
×
10

7
H
m
,
and
±
o
≡
1
μ
o
c
2
,
where
c
≈
3
×
10
8
m/s is the speed oF
light in Free space.
(In Gaussiancgs units
B
c
is used in
place oF
B
, while
±
o
=
1
4
π
and
μ
o
=
1
±
o
c
2
=
4
π
c
2
.)
– magnetic Feld
B
describes
by defnition
an additional force per unit
charge which is experienced when
q
is in motion with a ±nite
v
within
the frame of reference where
E
is measured (typically called the “lab
frame”).
–
E
and
B
are related to and produced by distant charge carriers and
their motions as described by
Maxwell’s equations
(see margin),
which e²ectively reduce, in static cases (i.e., nontime varying cases),
to
Coulomb
’s and
BiotSavart laws
(to be reviewed shortly).
–
In the MKSA system where
q
is measured in coulombs (C) units,
E
is
in Nt/C=V/m and
B
in V.s/m
2
=Wb/m
2
=T, where Nt, V, Wb, and T
are abbreviations for newtons, volts, webers, and teslas, respectively.
•
Particle positions
r
, velocities
˙
r
, and accelerations
¨
r
,
as well as
forces
F
and ±elds
E
and
B
are described in terms of
3D vectors
. In
Cartesian
coordinates
such vectors and vector functions are expressed in terms of
mutually
orthogonal
unit vectors
ˆ
x
,
ˆ
y
, and
ˆ
z
as in
r
=
x
ˆ
x
+
y
ˆ
y
+
z
ˆ
z
≡
(
)
and
E
=
E
x
ˆ
x
+
E
y
ˆ
y
+
E
z
ˆ
z
≡
(
E
x
,E
y
z
)
etc.,
where
1
Quantum models (as opposed to classical) describe the likelihood of detection of charge carriers
at locations
r
(as opposed to their speciFc trajectories), depending on applied force Felds
F
and related potentials — quantum approach remedies the shortcomings of classical models
based on Newton’s dynamics at atomic and smaller scales.
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 Spring '08
 Kim
 Law, Charge, Magnetic Field, Electric charge

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