Laser Imaging Laboratory : www.chosun.ac.kr/~yjshin
Professor of Physics, Chosun University
[email protected] 82-62-230-6638
Yong-Jin Shin, Ph.D.
ELECTROMAGNETICS - II
— ELECTROMAGNETICS —
1. Vector Analysis
2. Electrostatic Field in Vacuum
3. the Electrostatic Field; Energy and Potential
4. Conductors in Vacuum
5. Dielectric Materials
2nd semester
1st semester
6. Electric Current
7. Magnetic Fields
8. Magnetic Circuits
9. Electromagnetic Induction and Inductance
10. Electromagnetic Field
ROUGH COURSE CONTENTS (2nd semester)
EXAM : will be given during midterm- and final-exam week
6. Electric Current
7. Magnetic Fields
8. Magnetic Circuits
9. Electromagnetic Induction and Inductance
10. Electromagnetic Field
LITERATURES :
Schaum’s Outline of Electromagnetics –Joseph A. Edminister– McGraw-Hill (2011)
Introduction to Electrodynamics-David J. Griffiths-Pearson(2014)
Classical Electrodynamics– J.D. Jackson – John Wiley & Sons
전기자기학 – 심광열 외 공저 – ㈜북스힐 (2008)
전자기학의 기초 – 신용진외 공저– ㈜북스힐
Outline and Object of Subject
Electromagnetic theory, together with classical and quantum
mechanics, forms the core of present-day theoretical training
for undergraduate and graduate physicists. A thorough
grounding in these subjects is a requirement for more
advanced or specialized training.
Typically the undergraduate program in electricity and
magnetism involves two semesters beyond elementary physics.
with the emphasis on the fundamental laws, laboratory
verification and elaboration of their consequences, circuit
analysis, simple wave phenomena, and radiation. The
mathematical tools utilized include vector calculus, ordinary
differential equations with constant coefficients.
01 week Chapter 6. Electric Current
(1/2) Current Flow, Electric Resistance
02 week Chapter 6. Electric Current
(2/2) Voltage, Power, Thermoelectric Phenomenon
03 week Chapter 7. Magnetic Field
(1/3) Magnetism, Magnetostatic Field
04 week Chapter 7. Magnetic Field
(2/3) Magnetic Potential, Magnetic Dipole
Content of Study
05 week Chapter 7. Magnetic Field
(3/3) Current-produced Magnetic Fields, Magnetic Force
06 week Chapter 8. Magnetic Circuit
(1/2) Magnetization Phenomenon, Demagnetizing Force
07 week
08 week Midterm Examination
Chapter 8. Magnetic Circuit
(2/2) Boundary Condition for Magnetic Material,
Magnetic Circuit
Content of Study
09 week Chapter 9. Electromagnetic Induction and Inductance
(1/3) Faraday’s Law of Induction, Self- & Mutual-Induction
10 week
11 week
12 week Chapter 10. Electromagnetic Field
(1/3) Electromagnetic Waves, Displacement Current
Content of Study
Chapter 9. Electromagnetic Induction and Inductance
(2/3) Induced Electromotive Force, Calculating Inductance
Chapter 9. Electromagnetic Induction and Inductance
(3/3) Energy stored in the Coil, Work by EM Force
13 week Chapter 10. Electromagnetic Field
(2/3) Maxwell’s Equations, Traveling EM Waves
14 week Chapter 10. Electromagnetic Field
(3/3) Reflection and Refraction of Electromagnetic Wave
15 week Final Examination
Content of Study
Chapter 6. Electric Current
[email protected] www.chosun.ac.kr/~yjshin
A. Current Flow
B. Electric Resistance
C. Voltage
D. Joules Heat and Electric Power
E. Thermoelectric Phenomenon
Yong-Jin Shin, Professor of Physics, Chosun University
1. Moving Charge (e+ ; positive electron) :
Moving in the same direction as the current
2. Current I (or i) is not a vector
3. Current density J (or j) is a vector
Direction of a J is the direction of an I
◈ Definition of Current
• Any motion of charge from one region to another in conducting
materials
◈ Direction of a Current
Current
• The SI unit of current is the ampere. i.e., Current is the amount
of charge flowing through a specified area, per unit time.
electron moving
current direction
(1 ampere = 1 coulomb/sec) dt
dQI
(1/2)
Current
The same current can be produced by
(a) positive charges moving in the
direction of the electric field E or (b)
the same number of negative charges
moving at the same speed in the
direction opposite to E
The current I is the time rate of charge
transfer through the cross-sectional area A.
The randum component of each moving
charged particle’s motion averges to zero,
and the current is in the same direction as
E whether the moving charges are positive.
◈ Microscopic Model of Current
(2/2)
◈ Definition of Current Density
• The current I through an area S depends on the concentration n
and charge q of the charge carriers, as well as on the magnitude
of their drift velocity vd. The current density is current per unit
cross-sectional area.
(ampere/m2) dnqvS
IJ
◈ Current density(vector) vs. Current(scalar)
dSJIS
IJ
SnqvSvnqIvnqJ ddd
Current Density
Drift Velocity / Speed
◈ Drift Velocity / Speed
We can express current in terms of the drift velocity of the moving charges.
Let’s consider the situation, a conductor with cross-sectional area S and an
electric field E directed from left to right. To begin with, we’ll assume that
the free charges in the conductor are negative(−); then the drift velocity is in
the direction opposite to the field.
dvltandenSlQ /)(
Senvvl
nSle
t
QIso d
d
)/(
,
S
IJwhere
en
J
enS
Ivthen d ,,
Cewith 1910602.1,
SenvI d
denvJ
For the current density …….
Steady Current and Charge Conservation
◈ Continuous Equation
Conservation current density
Continuous boundary condition
from steady current dt
dqI
and JdsIs
IJ
then t
J
“Continuous Equation”
(time dependent charge distribution)
0 J If = 0
(time independent charge distribution)
so
dV
tdt
dqsdJ
dVJsdJ
with, Gauss theorem
It is defined as the ratio of the voltage applied to the electric current which
flows through it :
Electrical resistance is the opposition to the passage of an electric
current through that conductor. It varies with types of conductor ,
thickness, length, and temperature.
Resistance and Resistivity
◈ Resistance
(1 = 1 Volt/Ampere) i
VR
R
Vi
◈ Resistivity
If conductor has cross section S[m2] and length l[m], the resistance R is
][S
lR ][ m
l
SR
(definition of resistivity)
Electric Conductivity
Conductivity(k=) varies depending on the material, physical state and
temperature dependent.
◈ Conductivity
◈ Ohm’s Law
The electric current passing through a conductor is directly proportional to the
potential difference across it, and is inversely proportional to the resistance.
S
IJ with
S
lRand
R
VI
l
Vk
l
V
l
S
S
V
RS
VJ
1with
l
VE
]/[ 2mAE
kEJ
so,
11 m
RS
lk
with
R
VI IRV
EkEJ or, 1kwith
1/2
• Conduction electrons in the metal treated with gas molecules.
• Receiving acceleration of mass m electron by electric field (Newton’s 2nd Law)
• Drift velocity / speed
when is the average amount of time it takes to collision then collision,
mEe
mFaamEeEqF
m
eEavd
ne
Jvd
also,
so, Jne
mE
ne
J
m
eE
2
k
JJE also,
then,
dmv
ne
m
nek
221 (with, ; mean free path) dv
◈ Conductivity of Metal
Electric Conductivity 2/2
Temperature Coefficient of Resistance
◈ Temperature Coefficient
Let R0 is the resistance of conductor at temperature 0℃. When 1℃ rise
in the temperature of the conductor, the growth rate of the resistance α0
is the temperature coefficient at temperature 0℃.
][1 00000 tRtRRRt with 5.234
10
Rt is the resistance of the conductor at temperature t℃
][1 tTRR ttT with
t
tT
tR
tT
RR
Rt is the resistance of the conductor at temperature t℃ and RT is the
resistance of the conductor at temperature T℃.
When 1℃ rise from t℃ in the temperature of the conductor, the growth
rate of the resistance αt is the temperature coefficient at temperature t℃.
Electric Resistance and Capacitance
◈ Parallel Plate Capacitor
QndsE
s ‘Gauss’s Law’
◈ Micro Current in the Dielectric
kEEJ
1 Where, ρ : resistivity
k : conductivity
for the dielectric
CVQEdsJdsJSI
ss
111
ks
l
s
lR
RC
CR
I
CV
l
s
RC
◈ Resistors in Series
eqiRRRRiiRiRiR )( 321321
The current i must be the same in all of them.
j jeq RRRRR 321
Equivalent Resistance
◈ Resistors in Parallel
eqRRRRRRRiiii
321321
321
111
The potential difference between the terminals of each resistor must be the same and equal to ɛ
j
jeq RRRRR
11111
321
Equivalent Resistance
Kirchhoff’s Rules
The algebraic sum of the currents into any junction is zero.
◈ 1st Rule (Junction Rule, valid at any junction)
Multi-loop circuit Charge Conservation
0321 j jiiii
at b junction
0321 iii
at d junction
0321 iii
Let out (+) and in (-)
231 iii
(1/2)
The algebraic sum of the potential differences in any loop, including
those associated with emf’s and those of resistive elements, must
equal zero.
Single-loop circuit Energy Conservation
221121 RiRi j jjj j Ri
iR
Let clock-wise (+) and
counter clock-wise (-)
0 iR
Kirchhoff’s Rules (2/2)
◈ 2nd Rule (Loop Rule, valid for any closed loop)