This preview shows pages 1–3. Sign up to view the full content.
ECE 329 Lecture Notes — Summer 09, Erhan Kudeki
1 Vector felds and Lorentz Force
•
Interactions between charged particles can be described and modeled
1
in terms of
electric
and
magnetic
felds
just like gravity can be
formulated in terms of
gravitational felds
of massive bodies.
–
In general, charge carrier dynamics and electromagnetic Feld vari
ations
2
account for all electric and magnetic phenomena observed
in nature and engineering applications.
•
Electric and magnetic Felds
E
and
B
generated by charge carriers —
electrons
and
protons
at microscopic scales — permeate all space with
proper time delays, and combine additively.
±
2
±
1
1
2
x
±
2
±
1
1
2
y
–
Consequently we associate with each location of space having Carte
sian coordinates
(
x, y, z
)
≡
r
a pair of timedependent
vectors
E
(
r
,t
)=(
E
x
(
r
)
,E
y
(
r
)
z
(
r
))
1
Interactions can also be formulated in terms of
past locations
(i.e., trajectories) of charge carriers.
Unless the charge carriers are stationary — i.e., their past and present locations are the same — this
formulation becomes impractically complicated compared to Feld based descriptions.
2
Timevarying Felds can exist even in the absence of charge carriers as we will Fnd out in this course
— light propagation in vacuum is a familiar example of this.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documentand
B
(
r
,t
)=(
B
x
(
r
)
,B
y
(
r
)
z
(
r
))
that we refer to as
E
and
B
for brevity (dependence on position
r
and time
t
is
implied
).
Maxwell’s equations
:
∇·
E
=
ρ
±
o
B
=0
∇×
E
=

∂
B
∂t
B
=
μ
o
J
+
μ
o
±
o
∂
E
.
such that
F
=
q
(
E
+
v
×
B
)
,
with
μ
o
≡
4
π
×
10

7
H
m
,
and
±
o
=
1
μ
o
c
2
≈
1
36
π
×
10
9
F
m
,
in mksA units, where
c
=
1
√
μ
o
±
o
≈
3
×
10
8
m
s
is the speed of light in free space.
(In Gaussiancgs units
B
c
is used
in place of
B
above, while
±
o
=
1
4
π
and
μ
o
=
1
±
o
c
2
=
4
π
c
2
.)
•
Field vectors
E
and
B
and electric charge and current densities
ρ
and
J
— describing the distribution and motions of charge carriers — are
related by (i.e., satisfy) a coupled set of linear constraints known as
Maxwell’s equations,
shown in the margin.
–
Maxwell’s equations are expressed in terms of divergence and curl
of ±eld vectors — recall MATH 241 — or, equivalently, in terms
of closed surface and line integrals of the ±elds enclosing arbitrary
volumes
V
and surfaces
S
in 3D space, as you have ±rst seen in
PHYS 212.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Kim
 Electromagnet

Click to edit the document details