PowerPoint by Dr. Cheng
Ver. 1: Feb. 27, 2015
Welcome to this
Credit/Hours 3/4 Day/Time , , 8
Department School of EEE (Soph.) Location P208
Instructor Yisok Oh Tel. 320-1481 e-mail yisokoh@hongik.ac.kr
Office Hour P607, Office Hours: 7
T.A. ******** Park,
1. Course Description
This course covers the basic theories and fundamental concepts on the principles and
applications of static electric and magnetic fields and all kinds of phenomena relating to the
static electromagnetics. At first, the vector differentiation and integration will be introduced
as the background mathematics for the forth-coming electromagnetic field analysis. Then,
the electrostatics and magnetostatics will be taught in this course, which are emphasized
on field computations, Maxwell's equations, boundary conditions, design principles of the
circuit elements (R, L, C), and material characteristics.
Syllabus
3
sley
Reference
book
ioli, 6th Ed., Pearson
Grade
Distribution A+/A0 : 20~30%, B+/B0 : 30~40%, C+/C0 : 20~30%, D+/D0/F :
Grading Mid-term Exam 40%, Final Exam 40%, Assignments 10%, attendance 10%
Exams A midterm exam and a final exam.
Assignments 6~8 Assignments
Pass/Fail
Criteria
'F' grade will be given to the students (a) Cheating, (b) Attending less than
2/3 of all classes, (c) not taking either exam.
Course Retake
Policy The highest grade will be B+ for the students retaking this course.
4. Teaching Format and Other Announcements
Teaching Format Beam Project,
Announcements TA Hour: ?
1 Overview of Electromagnetics, Vector Multiplication 1.1-1.3, 2.1-2.3
2 Orthogonal Coordinate Systems 2.4
3 Gradient, Divergence, Divergence Theorem 2.5-2.7
4 Curl of a vector field, Stokes’s Theorem, Null identities 2.8-2.11
5 Electrostatics, Coulomb’s Law 3.1-3.3
6 Gauss’s Law, Electric Potential 3.4-3.5
7 Conductors and Dielectrics, Electric flux density 3.6-3.7
8 Boundary Conditions, Capacitances, mid-term Exam 3.8-3.9
9 Boundary-value problems 3.10-3.11.4
10 Method of lines, Steady electric current, Ohm’s law 3.11.5, 4.1-4.4
11 Electric current, Resistance 4.5-4.6
12 Magnetostatics, Vector magnetic potential 5.1-5.3
13 Biot-Savart Law, Magnetic dipole 5.4-5.6
14 Magnetic field intensity, Inductance 5.7-5.10
15 Magnetic energy, force, torque, Final Exam 5.11-5.12
Honor
Code
You are expected to do your own work in all aspects of this course and all submitted
work must be original. (No cheating)
Syllabus -continued-
Maxwell’s
Antenna
Design
(Senior):
Power dividers, Hybrids,
Filters, Resonators, etc.
Electric Circuit
How:
7
and others
: = Principle, Function, = Energy, Force. ()·() :, , , ,
Electromagnetic Fields: Spatial Distribution
() , Eectro magnet ics
What do we study in ‘Electromagnetics’?
(“ ”, “~ ”)
(Soccer Field, “(golf) Field”)
(2) Don’t ask me. How do I know?
(3) To learn about the principles on all areas related with
electricity and magnetism; i.e., Electronic Circuits, Electric
Machinery, Semiconductors, Controls, Communications,
Engineering.”
9
10
(page 4, Fig. 1-1):
(peta)
(exa)
(pico)
(femto)
11
Charge : Q, q (C) Coulomb, electron charge: e = 1.6 X 1910
E
H
,(V/m) Voltage
Ch. 2: Vector Analysis (Vector differentiation and vector integration)
Ch. 3: Static Electric Fields
Ch. 4: Steady Electric Currents
Ch. 5: Static Magnetic Fields
An electron: q=-e
on the cover sheet ]
13
D
B
Tesla
3
2
2
dt
14


Permittivity of free space
Permeability of free space
light velopcity (m/s)in freespace8

Notations for vector differentiations.
Vector : magnitude and direction ; Electric field , force , velocity , etc.
Circuit theory – all scalar (complex)
Field theory – Scalar , Vector (complex)
(1) Vector algebra (multiplication)
(3) Vector differentiation & Vector Integration
Lecture 3
)(,
2-3.1 Dot product
cos ( ) cos projection of onA B AB scalar B B A
)1cos1(
cos
cos0
A
A A A A
ABAB sin
Area of parallelogram
)()( producttriplescalarscalarCXBA
n
n
x y
Lecture 4
ˆ ˆ ˆx y zA A x A y A z
24
ˆ ˆˆy z x,
ˆ ˆ ˆ ˆˆ ˆz x y, ( x z y )
ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆˆ ˆx x 1 y y 1 z z 1 x x x x cos0 1





25
vector
(0,0,0)originthefromstartalways
zzˆ
ˆ ˆ ˆx y zA A x A y A z
26
dl
forSurface integral of vector fields
for volumeintegral of vector fields
2 ˆds ? ydxdz
x y z x y z
x x y y z z
ˆ ˆ ˆ ˆˆ ˆA B ( A x A y A z ) ( B x B y B z )
A B A B A B A B

x y z x y z
y z z y z x x z x y y x
x y z
x y z
ˆ ˆ ˆ ˆˆ ˆA B ( A x A y A z ) ( B x B y B z )
ˆ ˆ ˆx( A B A B ) y( A B A B ) z( A B A B )
ˆ ˆ ˆx y z
A B A A A
B B B
29
Lecture 5
r z
r z
Dot product
A B A r A A z B r B B z A B A B A B
Cross product
r z
B B B
ˆ ˆ
33
ˆ ˆˆ
ˆ ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ 0 ˆ ˆˆ
ˆ ˆ ˆ ˆsin cos sin sin cos
ˆPosition vector ;














Rd
dRsin
dR
ds1
ds2
ds3
dl
35
and cos cos cos sin sin
sin cos 0
wavesphericaltypesphere
sin,,:)ˆ,ˆ,ˆ(:Spherical
waveguidecirculartypecylinder
,,:)ˆ,ˆ,ˆ(:lCylindrica
general;,,:)ˆ,ˆ,ˆ(:Cartesian
Summary
Antenna Analysis
x
y
ˆ ˆsin cos sin sin cos ˆ ˆcos cos cos sin sin
ˆ ˆsin cos 0
)(directiondirectionˆinratechangemax n
Electric potential in a region,
Temperature distribution, etc.
shortest distance between the two
surfaces (P1 to P2)
l n
Constant V
Let us consider a scalar field, V(x,y,z)
Then, we may need to describe the space ‘rate of change’ of the scalar field at a
given point dependent on direction
a vector is needed to define the space rate of change.
Point P1 is on surface V1, and P2 is on
surface V1+dV along the normal vector dn
P3 is a point close to P2 along dl.
Space rate of change = dV/dl
: directional derivative (dependent on
the direction of dl)
39
z
40
Gradient ; derivatives of a Scalar field Vector
Divergence ; derivatives of a Vector field Scalar
Curl ; derivatives of a Vector field Vector
p. 41 [at (a), on the fourth line, e-1 is missing.]
41
in out
Same source
(No divergence)
“Divergence”: Net outward flow of the field (flux) per unit volume
: means a Source in the volume (or a sink)
s outward unit normal vector
v
enclosing a volume
42
0 0 0Consider a centered about ( , , )v x y z P x y z
zAyAxAA
fieldvectoraA
( , , ) ( 2
face face face face face face
front x face
A ds A ds
x i A ds A xdydz A x y z y z y z
x y z



2 2
A Ax x y z
x x
0 B
; total outward flux through the surface
Divergence Theorem
Summation:
47
integralline;
contouraround
ofnCirculatio
fieldsvectorofncirculatio
;sourceVortex
c
dlA
C
A
Surface integeral (flow source)
Q
Divergence (flow source)
Example 2-14 (p. 53) Calculation of the circulation of a vector.
48
0
u
n
direction
otherany
:ACurl Measure of the strength of a vortex source (circulation) defined at a point,
(small contour) such that the circulation is a maximum.
(Remember that maximum space rate of increase Gradient)
:nˆ 1
lim max0
Differentiation
Maximum net circulation of the vector A per unit area in n-direction
49
A dlF When we use rectangular coordinate, we must use
difficult integral formulae (using an integral table).
Lecture 10
22222 9,9)3,0(3 yxxyyxyx
52
In a), e-1 is missing.
-. Example 2-5
21212212212 ˆsinˆˆ 21

0 0 0 0 0 0
( ) , , , , 2 2 2
ˆ, , , , 2 2
right right z side side
y z z i A dl A A x y z z z z
dl zdz
y y A x y z A x y z






refer to “back cover”
Example 2-15 (p. 58)
c s
jj jc
A s A dl s
C
Consider an open surface, Or,
.
.. .
Example 2-16 (p. 60) Verification of the Stokes’s Theorem.
RHS
59
0contourclosedovervariationScalar
60
potentialscalarelectric;V
)(intensityfieldElectric;E
AB
A
BB
VEVE
V
EE
0,0,generalin;exampleFor
0,0;vectoralirrotationnorsolenoidalNeither.4
0,0;vectorsolenoidalnotbutalIrrotation.3
0,0;vectoralirrotationnotbutSolenoidal.2
0,0;vectoralirrotationandSolenoidal.1
A B B A A B
A A A
Coulomb’s Experiment (in 1785) “Coulomb’s Law”
Gauss developed “Gauss’s Law” Maxwell’s Equations
3-1 Overview Stationary electric charges Static electric fields (not changing with time)
In Ch. 3, we derive the Maxwell’s equations & boundary conditions, compute the electric
fields, electric potentials, material characteristics, capacitances, energy and forces.
3-2. Fundamental Postulates of Electrostatics in Free Space
Electric field intensity : force per unit charge In a region where an
electric field exist









0
0
(Differential form) Gauss’s
s
*Kirchhoff’s Voltage Law
(algebraic sum of voltage drop around any close circuit is zero)
Ch. 3 Static Electric Field Lecture 14
3-3 Coulomb’s Law

ddRRsd sin ˆ 2
Consider a point charge +q at the origin of spatial coordinate
+q
66
If the charge q is not located at the origin
pq q
RRR ERddREddRRREsdE 2 2









2112212 q qEqF at of to due by dexperience Force : where
1q 2q
r
2
21
69
Determine the electric field intensity at P(-0.2, 0, -2.3) due to a point charge of
+5(nC) at Q(0.2, 0.1, -2.5) in air. All dimensions are in meters.
Example 3-1
mVq RR
RR EP /
Example 3-2 The electrostatic deflection of a cathode-ray oscilloscope is depicted in Fig. 3-2
Electrons from a heated cathode are given an initial velocity by a positively
charged anode (not shown). The electrons enter at into a region of deflection
plates where a uniform electric field is maintained over a width w.
Ignoring gravitational effects, find the vertical deflection of the electrons on the
fluorescent screen at .
, C106.1 19 eq kg 109.1m -31
Assuming gravitation force is negligible, ge FF
(i) Electric field ; dd EyE ˆ
dt
CtE m
e dttE
1
2
00
2
0
210
0
3-3.1 Electric Field due to (a system of) Discrete Charges
Vector
summation
R R
3-3.2 Electric Field due to a Continuous Distribution of Charge
E(1) Volume charge density: )/( 3mCv
R R
1
s sdR R
E ˆ 4
l ld R
mCl /
Determine the electric field intensity of an infinitely long, straight, line charge
of a uniform density in air.
l
x
y
z
??E
(ii) use
R z z
ˆ ˆˆ ˆˆˆ ˆ, ˆ ˆ
rr z z rr z z R R R rr z z R
rr z z r z


4 ( )
r z r z
02 2 3/ 2 2 2 3/ 2 0 0
ˆ 1 ˆ ˆ 2
4 4[ ] ( )
r z r z


r zr z
Easy when we use the Gauss’s Law. (Example 3-4)
22 zr
Good for a uniform
direction of electric fields
78
Example 3-4 Use Gauss’s law to determine the electric field intensity of an infinitely
long, straight, line charge of a uniform density in air.l
1S
2S
z
x
y
s s ss
(iii) Integrate on S
0 0 31 sdEsdE
2 2
Q L Q dv x y

79
Example 3-5 Determine the electric field intensity of an infinite planar charge with a uniform
surface charge density .s
* Cartesian coordinate Gaussian Surface
* 0
1ˆˆ nz
zn ˆˆ2
yn ˆˆ3
21







Given:

Energy Conservation ; 0 E (Maxwell eqn.)
VE
VE
V increasing V electric potential.
; work done in carrying a charge from one point to another
)(V
1221 VVV potential difference (electrostatic voltage) between P2 and P1
2211 0 VVV (absolute potential)
ground, or at infinity
q q
q
E
VR
q
q
d
x
R R
1 1 1 1 [ ]
4 4 cos cos
q d qd

ˆˆ 2cos sin / , 4
R R
R
0 0 0 0
R R R R
Example 3-8 (DIY)
Find E for a circular disk charge at a point on z-axis using potential V
85
Conductors : -high conductivity
Semiconductors : medium conductivity
conductor Dielectric (insulator)
0v
Inside ; 0v according to Gauss’s Law 0 E
Static ; no movement of charges no tangential Electric field
nEE n ˆ (always normal) is normal to constant V V
Conductor surface : equipotential surface
Inside ; (same potential) 0E
0 0 0
Boundary Conditions:
87
1 2 3
SQ E n ds E n ds



Boundary condition on

Find and .E V
0)( 2 0
02 E
R
(3)
3 0 0
4 4
i R
Q R R E
Q Q Q V V V V
R R R








nonpolar molecules
21
(C )p qd m
2ˆ ( / )ps P n C m
2. Equivalent polarization volume charge density, pv
Net charge “remaining” in , (“+” for ‘flowing out’)V
ps ˆ pvs s s v v Q ds P n ds P ds P dv dv
Divergence thm.
Total charge for neutral dielectric body :
ˆ 0ps pvs v s vQ ds dv P n ds P dv
2 2 2 00 0
ˆ ˆ ˆ1 =
44 4 v
dp R P R P R dV dv V dv
R R R
In free space, 0
0 00
Define , 2 0 , : ( / )D E P D C m “Electric flux density”
(electric displacement) 3/ mCD v : v Free charge (source)
Maxwell’s Equation
0 0 0 0
E E C m
Gauss’s Law
“total outward electric flux over any closed surface”=“enclosed total charge”
93

3-7.1 Dielectric Strength Dielectric strength = maximum that a dielectric material can withstand
without dielectric breakdown. E
For example, (Table 3-1)
dE
kV 9 . 22
Very high E
Simple media if the dielectric constant is linear, homogeneous, and isotropic.
Example 3-11 (Charge distribution on two spherical conductors) Example 3-12 (Dielectric strength of a Coaxial cable) DIY
linear ; is independent of
isotropic ; is independent of direction of
E
We learned B.C for air – Conductor interface ; 0
, 0
as
or s
snns DDDDn 21212 , ˆ
Dielectric : No free charge
snn EDD 1112 0
2n
96
Example 3-13 Determine Ei, Di, and Pi inside the Lucite () (DIY)
Example 3-14 (p. 114)
)0( s
Find 2E
22 , E
(1) 1 2 1 1 2 2 sin sin (1)t tE E E E
(2) 1 2 1 1 2 2
1 1 1 2 2 2 cos cos (2)
n n n nD D E E
E E
12 2 1 2 1 2
2 1 1
2 2 2 1 1 1 1 1 2
1 1 tan tan tan tan tan ( )
( sin ) cost nE E E E E E







Determine: E2 on a boundary point P2.
Skip:
97
: unchanged for
F V
Q C
depends on geometry and filling material
Lecture 22
(1)Choose coordinate system Cartesian coordinate
(2) assume charges +Q and –Q
EEDQsdD rs 0 ,
QS
1S
Gaussian
surface
E
+Q
-Q
99
(3) Find E= - grad V
(4) Find Q using Gauss’s Law
(5)Find C
Another Approach:
(5) Find C,
(2)+Q inner conductor
1V 1Q
12R 2V
W V Work done to move from to a point.q
(sec. 3-5)
1 22112 VQVQW Potential energy
This work is stored in the assembly of the two charges: a potential energy
Assume a third charge,
0 13 0 23
R R
0 12
1 2 2 2 2 2 1 2 1 1
0 12 0 12
R
Q Q W Q V Q Q W Q V
R R
0 12 13 23
R R R
V : volume including all charges
V
by the system ; ldFdW Q

12r
12R
E
E
dl
E
and
To find E
RR
Q sdE
(then,) How can we find (or ) ?V E
Use Laplace equation!! + Boundary specification Boundary value problem
02 V








5
; 2

& Spherical,
2
2
2
2
2
Example 3-21
(Find V at any points.) and Find VE E
(a) Determine potential and (b) surface charge density
0Given v y
y
dy
Vd
30 0 0
d d
0 0 0 0 0 0 0
0 0
d V d V d
d d
0 11





Example 3-23 Two concentric conducting shells.
2 1
1 2
(2) Poisson’s equation (or Laplace’s eq.) Some times,
(1) Charge distribution is not known.
(2) B.C. is not known (or, difficult to define B.C.) Method of Images
A. Point charge near Conducting plane
Example 3-24
Lecture 25
and 0ˆ, 12 yDnVE s
How about +Q ?
l lR
, r
(because V will be infinite with infinity.)
for the original line charge only
r
ri
Equipotential
iMOP common r
ri Constant, and
d a a
Ch.4 Steady Electric Currents Current : Conduction Current (motion of charges)
Displacement currents (Time-varying)
sec/10 3m
( drift velocity)
A) Convection current
SntuqNQ ˆ
ˆ ( ) Q


)/( 3mCv
: charge per carrier electron : e
u
tu
ii
N
i
where 2electron mobility, /e m v s
for copper, svme /102.3 23
, where , charge densitye e e e eJ u E N e
Let, )0( ee
: Conductivity (S/m) (Siemens/meter)
for Silicon, mS /106.1 3 (Semiconductor)
for Rubber, mS /10 15 (insulator)
)( 1
myresistivit
117
EJ
S l S S
0.0585.8 10 (0.001)
3
5.49 3.543.54 10 r m mm
r
( just moving )
V Q
I
S
Charge flow out ⇒ net Current, I ⇒ decrease of the charge Q in the volume
s v
vdv dt
dvJ )(
rtoffunctionv ,:
( )flow flow in out
j j

Equation of Continuity : t
v
t0
0
1
0
e

Under equilibrium condition (large t), 0 0 as v E t
In the interior of the conductor; Charge distribution 0, 0v E
121
(thermal vibration) Power dissipation
,W F l EqF
t t
drift velocity
1 1
( ) n n

Power density
(in Circuit Theory)
0 J
0 1
n J J
s s
I





2) Assume potential difference, Vo
3) Find
4) Find
Q b bV
l a a
C
Series resistance: 1
rd r
h
r
Ch.2 : Vector Analysis (Differentiation : )
:D Electric flux density (c/ 2m ) ED
mFair /10854.8)( 12
0 J
: magneto flux density Wb/ 2m ,T (Tesla)
Maxwell’s Eqns,
, ; ( / )mF qu B u velocity m s
Total EM force; ( ) ( )e mF F F q E u B N : Lorentz’s force equation
Moving charge = current Current produce magnetic field
JH Curl ; by Vortex source
5-2. Fundamental Postulates of Magnetostatics in Free space
H
. J
129
00 BsdB
H
B
From JH
S s c H ds J ds H d I : Ampere’s Circuital Law
( Integral form)
J C
Enclosed by C
Useful to compute
s
130
r b
Explanation for the toroidal coil in Example 5-2 (p. 1.75)
mH /104 7
132
Fringing fields (ignored)
(1) Cylindrical coordinate
c
A A J
A vector indensity
B A or H A find H from A




( ' )
A J A J
Surface enclosed by contour C
We are free to choose A by Helmholtz’s theorem (p.65)
0 ALet (and BA ) unique A
JA 2 : vector poisson’s equation
zz
yy
xx
JA
JA
JA

'
Vector magnetic potential,


2 2 2 0 ' ( ) ( ) ( )R R R x x y y z z
0R
R
''' IddSJdvJ
I
d
In Ch. 3,
2
0
Book cover AAA )(

( dx
dx
1 (( ') ( ') ( ') )x x y y z z
R
3
x x x x y y z z x x
R
3 3 3 2
ˆ ˆ ˆ1 ( ') ( ') ( ') ( ') 1ˆ( ) x x x y y y z z z r r R
R R R R R R

R R
R R
Example 5-4: DIY (p. 184) a square loop
138
R zz
R br
R z b
20 02 2 3/ 2
2 20 0 02 2 3/ 2 2 2 3/ 2
ˆ ˆ ˆ' ( ) '
ˆ ˆ' ( ) 4 2( ) ( )
R z b
z b
z b z b
R
From Example 5-6
R
B A
140
r
'R
Example 5-6 Find B at the distant point of a small circular loop
1
1
ˆ'
R R R
R rb
y R b zR
ˆ ˆ( sin ' cos ') ' ( )
I x y bd A r
R b R b R




(p. 186)
1sin,0cos
1
2 2 2 2 2 2 2 2 2 1
1 12 2 2 2 2
2
1 1 2 1 [1 sin sin ' ] (1 sin sin ')
R b b Rb R R
b b R b Rb R
RR
R R R R RR






')'cosˆ'sinˆ)('sinsin1( 1
''sin)'sinsin 1
(2)ˆ( 4
')'sinˆ)('sinsin1( 1
R R
q
q
d
Electric
Dipole
1
Ch. 3 Ch. 5
0 0 2 2
R R
In Ch.3 (3-6.2) (p. 103)
Polarization surface charge density:
=magnetization surface current densitymsJwhere ˆ ( / )msJ M n A m
2 0
145
mv i JM
Equivalent magnetization volume current density:
)()( 0 mvie JJBB
From H J
Magnetic moment density M produces an internal
flux density Bi which is proportional to M.
146
5-7 Magnetic field density H (A/m) and Relative permeability r
I


Then,
Let
Magnetic materials:
Instead rBB
Iron ; 770° C
HB , should satisfy the B.C on boundaries
(1) Apply 0 B 0 0 v s
Bdv B ds
1 2 2 1 1 2 2 1 2 1
lim 0 0
s h
B ds as h




2 1 2 1 2 1 1 2 2ˆ ( ) 0, n n n nn B B or B B H H
2n
1n
S
149
0
H t H t as h


ˆ 0 : /
ss h
J n when J where J A m


)( 1
)( 2
2n
1n
1H
2H
2 1 2
2 1 2
2 1 2
ˆ ˆˆ ˆ ˆ( ) ,
t H H J n t n n
n n H H J n A B C B C A
n n H H J n
n H H J if J
then n H n H H H





1121211
1B
11111 N
1 1 1
I I I
WLIW vvmm 2
Example 5-8 (p.203) Find L (self-inductance) of a toroidal coil
I
I
b-a
h
B
1. Choose coordinate system; Cylindrical coord. (r, , z) )ˆ,ˆ,ˆ( zr 2. Assume I is known
3. Find 1B From I (Ampere’s Law , or Biot-Savart Law)
Symmetric (and
N
s
sdB

dl dz z





)/( '
2 0
ˆˆ ˆ(1) . ( , , )
ˆ ˆ(2) ( ) , ( )
I on the surface only
Find B
B rd I
currents
x
x
x
x
B
ds
dz
dr
Example 5-10 (p. 205) Find L’ (per unit length) of a coaxial line.
I
I
B
consider AC current
Li dt
d emfV
1L 12L 1L
5.11.1 Magnetic energy in terms of Field Quantities BH ,
Electrostatics
Electric force :
magnetic force :
NEqFe
: , uNBuqFm velocity of a moving charge q 5-12.1 Current carrying Conductor.
u ld



two conductors,
1212 2112
(Biot-Savart Law)
Lecture 37
2
unit length
ˆ ˆ F I zdz B I z B
161
Torque
F
ld
ld
F
F
F
B
I
BldIFd
/ 2 2
1 1 ˆ ˆ 2 sin 2 cos 2
2 2
y
dT x I dl Bb dl b d x I b B d
T dT x I b B d x I b B d
xI b B
T m B N
163
Example 5-15 (p.218) Find and ,F T zByBxBB zyx ˆˆˆ
(use rectangular coord.)F
Ibbzm
BmT
21
13
ˆ
zFzF ˆ
Lecture 38
Fig. 6-6
5-12. 3 and in terms of stored magnetic EnergyF T
Mechanical work ldF
Force by flux
and
F W
W F










Ch.9 ; Wave guidance
(3 2)
Wireless Communication,