1 ไฟฟ้าสถิตย์ physics4
TRANSCRIPT
AJ. Suminya TeetaFaculty of Science Technology
Rajabhat Maharakham University (RMU)
4 32204
3
1.
.»»»
»
3. »»
»
Electrostatics :
( Electric Current) :
I
Ampere AMP.
Amp.Meter
Direct Current)
:
DC
12.
3.
4.5.
……………
?Thales of Miletus (600 BC)
: http://faculty-staff.ou.edu/
Benjamin Franklin (1706 -1790)
(fluid)
?( )
: http en wikipedia
:
(Static Electric)
•
•
•
•
???????
-
12
•
•
C : C
x1018
A s
(Electric Charges)
•
••
15
•
+
-
+--
+
17
e
q = Ne N
e = 1.6 x 10-19
C q = -e
q = +e
18
????????•
??????????
1.
2.
3.
****polarization
????
• 2
• 2
1.
•
•
2.
3. ( Induction)
•
???•
•
•
25
(Coulomb's
Law
• Charles Coulomb
21qqFe
2
1
rFe
260= (permittivity of free space) = 8
(Coulomb Law) (
1 2
12 21 2
q qF F F
re e
k= = =
9 9 2 2
0
18.9875 x 10 9 10 N m /C
4e
k xpe
= = @ ×
F12 q1
q2
q2 q1
r
12r̂
F12 q1
q2 q2 q11 2
12 122
q qˆF r
re
k=
q2q1
12F
q2 q112r̂
27
q qr
(a)
(b) 12r̂
(unit vector) qq
q qq
q2112 FF
q q q q
q q qq
q1
q2
q1
q2
1 2
12 122
q qˆF r
re
k=
28
q2 q1
q1
q2 q1
q1 q2
q2
q1 q2
12F
12r̂
1 212 122
q qˆF r
rek=
r
F12
F21
q1q2
r
F12
F21
q1 q2
(Attractive force)
(Repulsive force)
21r̂
212
12E21 r̂
r
qqkF
21F
29q1
q
+
1F
-
-q1
q2
r
r̂
12F
-
-q1
q2
r
r̂
13F
+
-q1
q3
r
r̂
q3
= +
1 2 1 2
12 12 122 2
12 1 2
1 2
1 23
1 2
q q q qˆ ˆF r r
r
q q( )
e e
e
k kr r
k r rr r
= =-
= --
12 1 2
1 2
12
1
ˆ
r r r
r rr
r r
= -
-\ =
-
2r
2q1
r
1q
12F
21F
1 2 1 2
21 21 212 2
21 2 1
1 2
2 13
2 1
q q q qˆ ˆF r r
r
q q( )
e e
e
k kr r
k r rr r
= =-
= --
x
y
z
31
q1 q2 q3
q3 q1 q2
32313 FFF
31F
32F
312310
1331 r̂
r4
qqF
322320
2332 r̂
r4
qqF
-
+-F32
F3
F31
q1
q2q3
r31
r32
31r̂
32r̂
32
n q1, q2,…,qn
qi
qi , qj (C) rij (m)
Fi , Fij (N)
n
ij
ij2
ij
ji
0
n
ij
iji r̂r
4
1FF
qi
iF
qi qjijF
ijr̂ (unit vector) qj
rij qi qj
1 1.0
1.0
1 2
2
9 2 2
2
9
9.0 10 / 1.0 1.0
(1.0 )
9.0 10
KQ QF
r
Nm C C C
m
N
1 C
34
2
-
x - m
1 2
2 e
q qF k
r
-19 11
1 2 1.6 10 , 5.3 10 q q e x C r x m
219
9 2 2 8
211
1.6 10 8.99 10 / 8.2 10
5.3 10e
x CF x N m C x N
x m
35
31 27
11 2 2
211
9.11 10 1.67 10 6.67 10 /
5.3 10g
x kg x kgF x N m kg
x m
473.6 10x N
839
47
8.2 102 10
3.6 10
e
g
F x Nx
F x N
1 2
2 g
m mF G
r
31 27
9.11 10 , 1.67 10 e pm x kg m x kg
36
C
3 q3
q1 qq1= q3=5.0
q2= 2.0 a = 0.1 mC
C
C
31F
32F
26 6
2 3 9
32 2 2
(2.0 10 )(5.0 10 )(8.99 10 ) 9.0
(0.1)e
q qF k N
a
6 61 3 9
31 22
0 0
31 31 31 31
0 0 231 31 2
3 31 32
3 31
(5.0 10 )(5.0 10 )(8.99 10 ) 11
2 (0.1)( 2 )
cos 45 , sin 45
cos 45 sin 45 11 7.9
7.9 9.0 1.1
7.9
( 1.1i 7.9j)
e
x y
x x
y y
q qF k N
a
F F F F
F F N
F F F N N N
F F N
N3F
37
4 q1 470 1,2,4) q2
250 3,3,0) q1 q2
1 2 1 2
2 221 21 21
21 2 1
1 2
3 2 1
2 1
q q q qˆ ˆF r r
r
q q( )
e e
e
k kr r
k r rr r
= =-
= --
21 2 1
2 1 2
2 1
ˆˆ ˆ2 4
2 1 4 4.58
r r r i j k
r r
= - = + -
- = = + + =
1 2
321 2 1
2 1
9 6 6
21 3
21
q qF ( )
ˆˆ ˆ(9 10 )(470 10 )(250 10 )(2 4 )F
4.58ˆˆ ˆF 21.97 10.99 43.94
ek r r
r r
x x x i j k
i j k N
- -
= --
+ -=
= + -
+
Qq3
+F
q2
+
F
q1 +
F
Electric field
Q
P ?
??
+
Qq3
+F
q2
+
F
q1 +
F
Q
?
?
??
?+
Qq0
+F
q0
+ + + +
+ + + + + +
+ + + + + + +
+ + + + + +
+ + + + +
+ +
+
+ +++
+ + ++++
+ + + ++++
+ + + +++
+ + +++
++0
00
limq
F
q
0/E F q=
VS
EF
E+
EF
E -+
EFE
-
EFE
--
Sourc
e o
f Ele
ctric
field
Test charge
000
limq
FE
q
***
?
00 q
F
q
FE
!!!!
0
0
2 2
0
/E F q
kqq kqE
r q r
=
= =
+q1
-q3
qn
+q4
-q2
E10
E20
En0
??
i
i
i
i
i
inP rr
qkEEEEE ˆ........
221
P
P (
•
•
–
•
Eqmdt
vda
y
y
1
47
(CRT)
• CRT
• CRT
49
•
Fe = qE = ma
a = qE /m
5 9.6x10-14 kg
2x106 N/C
+ + + + + + + +
- - - - - - - - - - -
E
FE
Fg
6 14 2
19
0
( ) 0
2 10 / 9.6 10 10 /
4.8 10
E g
E g
F
F F
F F
qE mg
q N C kg m s
q C
FE E
- 4.8x10-19 C
Electric line and Electric field
+
Q
ara
b
rb
2
a
ar
QkE
2
b
br
QkE
ba EE
a b
?
Electric field lines
B
Electric field lines
Electric field lines
Electric dipole
+ -
??????
?
•
6 q C q - C x
m P , m
61 9 5
1 2 2
1
62 9 5
2 2 2
2
5 5 5
5 5 5
(7.0 10 )(8.99 10 ) 3.9 10 /
(0.40)
(5.0 10 )(8.99 10 ) 1.8 10 /
(0.50)
3.9 10 j ; 1.1 10 i-1.4 10 j
1.1 10 i+2.5 10 j 2.7 10 /
e
e
qE k N C
r
qE k N C
r
N C
1 2
1 2
E E
E E E E
: P
P 2
+q0
y
x
7 A
q0
+
-
q1
q2
A
2 C
2 C
3cm
3cm 4cm
q = C
q1
21 EEE
1E
2E
E
q1 =q2 r1= r2 E1=E2
C
N1086.0ˆ
5
3
)105(
1021092 7
22
69
iE
5
3sin
5
4cos และ
+ A
1Ecos1E
sin1E
2E
cos2E
sin2E
jEiEE ˆsinˆcos 111
jEiEE ˆsinˆcos 222
jEE ˆsin2 1
rr
kQE ˆ
2
j
r
kqEA
ˆsin22
1
1
8
+q1
x
y
+q2
+q3
a
a
a
a a
2a
qq3
2E
3E
1E
3210 EEEE
q1= q2 = q3
10 EE
q2 = q3 r2=r3
jEiEE ˆsinˆcos 110
a
a2a
cos1E
sin2E 1E
rr
kQE ˆ
2
jr
kqi
r
kqE ˆsinˆcos
2
1
1
2
1
10
2
1cos
2
1sin
และj
a
kqi
a
kqE ˆ
22ˆ
22 2
1
2
10
• : ,
• : E
E
•
E E 2
kqE
r=
1.
dq dE
2
ii e
i
i
i
qE k
r
E E
2
2
ie
i
e
dqdE k
r
dqE dE k
r
9 l Q
Pd
dx dq
dE
2
dqdE k
x
Qdq dx dx
l
P dE
dE X dE
2
2 2
1 1 1
( )
e
l d l d
ee
d d
l d
ee e
d
k dqE dE
x
k dxdx k
x x
k lk k
x l d d d d l
(linear charge density) :
d
dq
Q
Q dq
d
dq d
(area charge density) :
dq
dA
A
Q
Q dq
A dA
dq dA
(volume
charge density) : V
Q
Q dq
V dV
dq dV
dq
dV
10
a
x
a +Qx
+Q
Q ds
ds
sQ
s
Q
+QQ dq
s dsl º =
ds dss
Qdsdq
dq1
dq2
x
dq1
dq2 dq1 = dq
+q0
y
x
1Ecos1E
sin1E
2E
cos2E
sin2E
1Ed
2dE
x
x
a
dq
Ed
cosEd
2
kdqdE
r=
cosE dE q= ò22 xar
22cos
xa
x
x a
E dE= òcosdE dE q=
( ) ( )2 2 2 22 2 2 2
0
Q
k dq x kQ xE
a x a xa x a x= =
+ ++ +ò
2222 )( xa
x
xa
kQE
xxa
kQE
23
)( 22
(1)
cosqdE
(Electric Flux)
:
E = E A
?
EAcosE
(Electric Flux)
E EA = 0o
E
E 0 = 90o
E
C
E
2
69
2E)1(
101)109(
r
qkE C/N1099.8 3
)6.12)(1099.8(EA 3
E/CmN1013.1 25
2 24 4(3.14)1 12.6r mp= = =. .
•
•
cosE i i i i iE A E A
( )
AdEAE i
i
iAi
E
..lim
0
Close surface
• (1), ; θ<90o, Φ
• (2), ; θ =90o, Φ = 0
• (3), ;90o
< θ <180o, Φ
EAcosE
N m /C
( )
AdEAE i
i
iAi
E
..lim
0
dAE AdE nE
En
Flux through a cubeE x
L
x
E dA
2
11
0
1
ELEAdAEdA)180(cosEAdE
0 2
2 2 2
E dA E(cos0 )dA E dA EA EL
00000ELEL 22E
A = L
L
L
?
?
?
surface
i
i
iA
AdEAEi
E
..lim
0
Gauss’ LawGauss’ Law
0
. in
surface
E
qAdE
E
0
= (permittivity of free space) 0
84
• qin E
E
E
AdE
0
inq ε
E
AdE
85
q
r
E=keq/r2
***Gaussian surface (
)
86
•
surface integral)
(Point Charge)
0
. in
surface
qAdE
E
Gauss’ law
88
q
S1
S1
S2 , S3q
q S1 S2
S3
0q /
0q /
89
90
•q
q
q
e2 2
o
q qE = = k
4πε r r
E
AdE
EdA in
o
q
ε
0
inqE dA
e=òÑ
2
0
4q
E πr ε
91
2
o
QE 4πr =
ε
Q
a r>a r<ar>a r
2
o
QE =
4πε r
E
AdE
EdA in
o
q
ε
dAE in
o
q
ε
92
r < a r
qin < Q
3 34 / 3 4 / 3
inqQ
a r
3 /inq Q r a
e2 3
o
QE = = k r
4πε r a
3/Q r a
3
2
0
/4
Q r aE r
E
AdE
EdA in
o
q
ε
93
o
λlE 2πrl =
ε
e
o
λ λE = = 2k
2πε r r
E
AdE
EdA in
o
q
ε
94
•
•
•2EAin
o o o
q σA σ2EA = 2EA = E =
ε ε 2ε
(Surface Charge)
02E
!!!
σ
(Area charge density)
96
2
0
4q
E πr ε 2
0
1 ,
4
qE
πε rRr
0,E Rr
q R
(r>R)
(r<R) 2
0
04 E πr
ε
E
AdE
EdA in
o
q
ε
AdE
R
97
-A
-
-
-
0
inE
qAdE
E
E EAcos
E
0
E
surface
E dA
98
R Q kEQ/r2
kEQr/R3
R kEQ/r2
Q 0 r < R
0
E2k / r
0/
0/ 2
q 5 C q -8 C q q2
P
2q3 q2 q1 q
q1=q3=2.0 q2= 3.0 a = 1 m
C C
100
http://www.rit.ac.th/homepage-sc/charud/selftest/2/index2.htm
1. q1 = q4q2 = q5 = -5.9 nC q3 = -3.1 nC
101
http://www.rit.ac.th/homepage-sc/charud/selftest/2/index2.htm
3, 4, 2, 1
2.
102
http://www.physics.sci.rit.ac.th/charud/oldnews/48/magnetic/OnlineTest_V4/index.asp
http://www.rit.ac.th/homepage-sc/charud/selftest/2/index2
2.
?
…..
?
gg UW
m
A B
r
?
Test charge
q0E
2,
qE k
r=
AB
ABr
qqk
r
qqkUU 00
( )
( )
r
qqkrU
12)(
r
qqkrU
12)(
.U F dsD = - ò
0 2.
kqU q dr
rD = - ò
r
?
r
qqkrUe
12)(r
mGmrU g
21)(
!!!!!
G (universal gravitational constant)
G = 6.67259 x 10-11
N.m2 / kg2
+Q
+10 μC
r
+20 μC
r
r
QqkrUe )(
+10 μC +20 μC
Constr
Qk
q
rUe )(
Q r
)()(
rVq
rUeEquipotential line
Test charge
q0E
000 q
W
q
W
q
UVVV exte
AB
2
00
r
QqkEqFF eext
V
AB
ABr
kQ
r
kQVV
:
+1 C
r
kQrV )(
?
000 q
W
q
W
q
UVVV exte
AB
111
•(equipotential surface)
B A
C B
B C
112
•
113
•
A B B A e
B A
1 1V -V = k q -
r r
e
qV = k
r
V = 0 Ar =
1/r
114
•
ie
i i
qV = k
r
V = 0 r = ∞
115
0
0
0 0
U q Ed
q EdUV Ed
q q
a+Q
-Qa
+Q
+Q
Ex. V -Q
+Q 3
P2
a
2 2 2 2
2 2
i
i
qV k
r
Q Q Q Qk
a a a a
kQ
a
Ex 9 (i) P (ii)
P
118
• dq
e
dqdV = k
r
e
dqV = k
r
V=0
119
• Q a P
x
eV = k
2 2 2 2
2e
πa k Qλ
x a x a
e
dqV = k
r 2 2e
dlk λ
x a
e edV = k k
dq λdl
r r
Q dq
d
L
[C/m] Pd [m]
P
dL
xd
dxk
r
kdqdV
xdx
dq = dx
)ln()ln()( 0
0d
Ldkxdk
xd
dxkdVV
LL
121
1 2
1 2
e e
q qV k k
r r
Q q
R r
1Q R
q r
122
1 2e
QE k
R2 2e
qE k
r
E1/E2
2 2 221
2 2 2
22
/
/
QE kQ R Q r Rr rR
qE kq r qR rR R
r
2 1
RE E
r
Q R
q r
123
A B) 0 d dE s E s
124
E V
e
qV = k
r
2e
qE k
r
125
•
1 2e
12
q qU = k
r
126
1 3 2 31 2e
12 13 23
q q q qq qU = k + +
r r r
127
μC
ก)P m
ข)q3=3.0
P
ค)
Ex. q1=2.0 µC
XY q2=-6.0 µC
m
128
1 2
1 2
ie e
i
q q qV k k
r r r6 6
9 2 2 2.0 10 6.0 10 8.99 10 /
4.0 5.0 p
x C x CV x N m C
m m
36.29 10 x V
f iU U U
0 i iU r 3f pU q V
6 3
3 0 3.0 10 6.29 10 0pU q V x C x V
21.89 10 x J
129
1 3 2 31 2
12 13 23
e
q q q qq qU k
r r r
25.48 10 x J
6 6
9 2 2
6 6 6 6
2.0 10 6.0 108.99 10 /
3.0
2.0 10 3.0 10 3.0 10 6.0 10
4.0 5.0
x C x Cx N m C
m
x C x C x C x C
m m
130
3.
•
(Capacitor)
capacitance)
131
Capacitor
132
•
133
(farad, F) Q
C =ΔV
135
•
136
QC =
ΔV
Q=
Ed o
Q=
Q/ε A d
oε A
=d
138
•
a b
QC =
ΔV
0
ln2
q bV
L a
02
qE
Lr
lne
=2k b / a
02
ln
L Lπε
b
a
140
•
a
b
e
1 1ΔV = k Q -
b a
e
Q abC = =
ΔV k b - a04
abπε
b a
b
e e
abC =
k k04
aπε a
b
a
b
r
a • C = a/k
•
•
143
•
144
Qtotal= Q1+Q2=C1V+C2V
1 2=eqC C C
1 2V=eqC C V C V
145
•
C2
C2
C1
C1
C2
C2
-Q
146
1 2Q Q Q
1 2
eq 1 2
Q QQ= +
C C C
1 2 ...V V V
1 2
1 1 1= + …
C C C
150
•
qdW = ΔVdq = dq
C2
Q
0
q QW = dq =
C 2C
22Q 1 1
U = = QΔV = C(ΔV)2C 2 2
151
•
2 21 1( )
2 2oU CV Ad E
21
2E o
Uu E
Ad
0 ,A
C V Edd
e= =
152
•
/o oC kC k A d
k
153
154
ก)
ข)
ค)
ง)
จ)
7.60 cm2
1.8 mm 20 V
A=7.60 cm2 , d=1.8mm, V=20 V V Ed
3
20
1.8 10
V VE
d x m
311.1 10 /x V m 11.1 /kV m
155
0
E 12 2 2 3
0 8.85 10 / 11.1 10 /E x C N m x V m
9 298.3 10 /x C m 298.3 /nC m
0
AC
d
4 2
12 2 2
3
7.6 10 8.85 10 /
1.8 10
x mx C N m
x m123.74 10x F 3.74 pF
QC
V
123.74 10 20 Q CV x F V
74.7 pC
21
2U CV
212174.7 10 20
2x C V
914.9 10x J 14.9 nJ
156
10
AB
1 2 3C C C C
10 10 10F F F
F
30 F
10 F
10 F
10 F
A B
157
3
18V C1
• C2 C3
c b
2 3 10 20 30cbC C C F F F
C1=15µF
C2=10µF C3=20µF18 V
aC3=20µF
C2=10µF
b
18 V
C1=15µF
a c
C abC1=15µF
a b
18 V
+Q -Q +Q -Q
C
+Q
18 V
-Q
• a b
158
1
1 1
1 1 1 cb
ab cb cb
C C
C C C C C
1
1
15 30
30 15
cbab
cb
F FC CC
C C F F
15 3010
45F F
QC Q CV
V10 18 180 F V C
•Q Q
•a b
…The End…