chapter 2.1 ~ 2.2 coulomb’s law electric field intensity · pdf file2017-03-14 1...
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2017-03-14
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Electromagnetics 1 (EM-1) with Prof. LEE
Chapter 2.1 ~ 2.2
Coulomb’s LawElectric Field Intensity
Week 2-2 (March 15)
Electromagnetics 1 (EM-1) with Prof. LEE
Charles-Augustin de Coulomb
Born 14 June 1736
Died 23 August 1806 (aged 70)
Nationality French
Fields Physics
Known for Coulomb's law
https://en.wikipedia.org/wiki/Charles-Augustin_de_CoulombCoulomb's torsion balance
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Electromagnetics 1 (EM-1) with Prof. LEE
Coulomb’s Experiments (about Force)
+Q1+Q2
R
F1 F2
F1=F2=F
F
Q2
F
R
Fixed Q1
Fixed Q1,Q2
Slope = k
when R=1m
~ 1/R2
where
0
0
Assuming that R >> d
dd
Electromagnetics 1 (EM-1) with Prof. LEE
Physical Insights: Point Charge Effect
Q1
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Electromagnetics 1 (EM-1) with Prof. LEE
Physical Insights: Charge Density Theorem
4πR2
+Q1+
Q2
R22
1
0 4
1Q
R
QF
πε=
=ρs ]/[ 2mC
][][
][
]/[
2,1
0
VFCQ
mR
mF
⋅=
ε
][ N
]/[][ mJN =
F
Test
charge
=Qt
Electromagnetics 1 (EM-1) with Prof. LEE
22
1
0 4
1Q
R
QF
πε=
Physical Insights: Electric Field Intensity
]/[
]//[]/[
]//[]/[
2
2
mV
mFmVF
mFmC
=
⋅=
22
1
0 4
1Q
R
QF
πε=
=ρs ]/[ 2mC
][][
][
]/[
2,1
0
VFCQ
mR
mF
⋅=
ε
][ N
]/[][ mJN =
=E1]/[ mV
2
04 R
QE
πε=∴
Electric Field Intensity
(Potential change in unit length)
]/[ mV
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Electromagnetics 1 (EM-1) with Prof. LEE
Physical Insights: E-Field Vector
4πr2
+Qr
2
04 r
QE
πε=
E = Ear
0
in Spherical
coordinates
Electromagnetics 1 (EM-1) with Prof. LEE
Physical Insights: Equipotential Contour
4πR2
+Qr r
QV
rr
Q
r
QE
0
0
2
0
4
1
44
πε
πεπε
=∴
==
E = Ear
0
]/[ mV ][V
Equipotential line (contour)
Potential
r
V
R
VE
∆
∆==⇒
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Electromagnetics 1 (EM-1) with Prof. LEE
Related Vector Calculation
r1 = x1ax + y1ay + z1az
r2 = x2ax + y2ay + z2az
r2 – r1 = (x2-x1)ax +(y2-y1)ay + (z2-z1)az
|r2 – r1| = (x2-x1)2 +(y2-y1)
2 + (z2-z1)2
Electromagnetics 1 (EM-1) with Prof. LEE
Related Vector Calculation
R = |r – r’| ar = |r – r’|
r – r’
r – r’ = (x-x’)ax +(y-y’)ay + (z-z’)az
|r – r’| = (x-x’)2 +(y-y’)2 + (z-z’)2
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Electromagnetics 1 (EM-1) with Prof. LEE
Related Vector Calculation for Multiple Charges
E1E2
Electromagnetics 1 (EM-1) with Prof. LEE
Chapter 2.3
Field arising from a Continuous VolumeCharge Distribution
Week 2-2 (March 15)
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Electromagnetics 1 (EM-1) with Prof. LEE
Related Vector Calculation
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Q
Volume (v)
Electromagnetics 1 (EM-1) with Prof. LEE
Example
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Electromagnetics 1 (EM-1) with Prof. LEE
Incremental E-Field and Charge Density
Electromagnetics 1 (EM-1) with Prof. LEE
Example
( ) φρρρπ
ddzdzQ
b
∫ ∫ ∫=0
4
2
1.0
0
22
)(
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Electromagnetics 1 (EM-1) with Prof. LEE
Important Physical Insights on Q(point), E, V
Q +
Q +
r
z
V
r
r
dr
dVE −=
E = Ear
r
VE
∆
∆−=
V
r∆
V∆+
0
2
04 r
QE
πε=
: Gradient (Chapter 4.4~4.6)
Slope=
Slope
Electromagnetics 1 (EM-1) with Prof. LEE
Important Physical Insights on Q(point), E, V
dr
dVE −=
r
QV
r
Qdr
r
QEdrLHS
VdVRHS
dVEdr
dVEdr
rr
V
Vr
0
00 2
00
0
00
4
4'
4'
'
''
πε
πεπε
=∴
−===
−=−=
−=⇒
−=
∫∫
∫
∫∫2
04 r
QE
πε=
Q +V
0r Chapter 4.4~4.6
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Electromagnetics 1 (EM-1) with Prof. LEE
Important Physical Insights on Q(point), E, V
dr
dVE −=
2
04 r
QE
πε=
r
QV
04πε=
Q
전기적영향력의
응집체
:Condensed Object
Of Electric Effects
=Charge
Q의공간적영향력
:Effect of Q in Space
=Potential
Q의공간적영향력의공간변화율
:Rate of Change in Space of Potential
혹은전하 Q의특정공간밀도
E = Electric Field Intensity
D = Electric Flux Density
4πr2
0ε
( )E
r
Q
Area
Q==
2
00 4πεεE = Ear
Q
E = Ear
= D
Electric Field Intensity
Potential
Charge
∫∫ −= dVdrE
Electromagnetics 1 (EM-1) with Prof. LEE
Example: Line Charge
dLdQ
uniformifL
Q
dL
dQL ==⇒ ρ
aρ
z∞
∞
( )
πρε
ρ
ρ
πρεε
2
2
0
00
L
L
E
L
Q
EL
Q
Area
Q
=∴
=
==
L
0
ρ
Chapter 2.4
E = Eaρ
E
V
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Electromagnetics 1 (EM-1) with Prof. LEE
Contents of the Chapter 2.
for Next (March 20)
as Week 3-1