1. 4
32204
AJ. Suminya Teeta
Faculty of Science Technology
Rajabhat Maharakham University (RMU)

2. Electrostatics)
1.
2.
3.

3. 1.





3

4. .
»
»
»
»
3.
»
»

5. Electrostatics :
( Electric Current) :
I
Ampere AMP.
Amp.Meter
Direct Current)
:

6. 1
2.
3.
4.
5.
……………

7. ?
Thales of Miletus (600 BC)
: http://faculty-
staff.ou.edu/

8. Benjamin Franklin (1706 -
1790) ?( )
(fluid)
: http en wikipedi

9. :
(Static Electric)

10. • ???????
•
•
•

11. 

-

12. (Electric Charges)
•

•

 C : C
x1018
A s 12

14. •
•
•



15. •

15

16. -
+
+ - -
+

17. 

e


q=
 N Ne
 e = 1.6 x 10-19
 C = -e
q
 q = +e 17

18. 






18

19. ????????
•
??????????

20. ????
1.
2.
3.
****
polarization

21. 1.
• 2
• 2

22. 2.
•
•

23. 3. (
Induction)
•

24. ???
•
•

25. (Coulomb's
Law
• Charles Coulomb

Fe q1q2
1
Fe
r2

25

26. (Coulomb La
r q1 q 2
q2 q1 Fe = F12 = F21 = ke
r2
ˆ
r12
F12 q1 F12 q1
q2 q2 q2  q1 q 2 q1
F12 = ke 2 r12 ˆ
r

F12 q2
r
ˆ12 q1 q2 q1
1
ke = = 8.9875 x 109 @9 x109 N ×m2 /C2
4pe0
0=
26
(permittivity of free space) =

27.  q1 q 2
q q F12 = ke 2 r12
r
ˆ
r
q1
q2
(a)
(unit
(b)
vector) q
ˆ
r12
q1 q
q q
q2   q
F12 F21
q q q q q
q q q 27

28.  q1q 2  q 2q1
F12 = ke 2 r12ˆ F21 k E 2 r21ˆ
 r r
F12
q2 q1
ˆ
r12 q1

F21 q2 q1
ˆ
r21 q1 q2
q2
(Repulsive force) q1 q2
(Attractive force)  
  F F
F12 F21 12 21
q1 q2 q1 q2
r r
28

29. q q3 q2 q3
2- -
+ +
ˆ
r ˆ
r ˆ
r
r r r 
= +
q1 -
F
-
13
q1 q1 -
 
F1 F12
q1 29

30.   
r = r- r
12
 1 2
 
r- r z
ˆ
r = 
12
1 2
 F12
r- 1
r q1
 
q1 q 2 q q2 r1
F12 = ke  2 r ˆ12 = ke  1  2 r12
ˆ q2
r12 r1 - r2
q q2   
= ke  1  3 (r1 - r2 )  F21
r1 - r2 r2
y
 q1 q 2 q q2
F21 = ke  2 r ˆ21 = ke  1  2 r21
ˆ
r21 r2 - r1 x
q1 q 2  
= ke   3 (r2 - r1 )
r2 - r1

31. q1 q2 q3
 
q3 q1 q2F31 F32
q1   
F3 F31 F32
-
r31 ˆ
r31
 q3q1
F31 ˆ
r31
 q2
q3 F32
4 2
r31
 -
ˆ
r32 0
r32 +
F31

F32
q3q 2
ˆ
r32
2
4 r32
 0
F3
31

32. n q1, q2,…,qn
 n q
i n qiq j
1
Fi Fij 2
ˆ
rij
j i 4 0 j i r ij

Fi
 qi
Fij qi qj
ˆ
rij (unit vector) qj
rij qi qj
qi , qj (C)
rij (m)
Fi , Fij (N) 32

33. 1
1.0
1.0
KQ1Q2
F
r2
9.0 109 Nm 2 / C 2 1.0 C 1.0 C
2
(1.0 m)
9.0 109 N
1C

34. 2
x - m
q1q2
- Fe k 2
r
19 11
- q1 q2 e 1.6 x10 C, r 5.3 x10 m
19 2
9 2 2
1.6 x10 C
Fe 8.99 x10 N m / C 2
8.2 x10 8 N
11
5.3x10 m
34

35. m1m2
Fg G 2
r
31 27
me 9.11x10 kg, mp 1.67 x10 kg
31 27
11 2 2
9.11x10 kg 1.67 x10 kg
Fg 6.67 x10 N m / kg 2
11
5.3x10 m
47
3.6 x10 N
8
Fe 8.2 x10 N
2 x1039
Fg 3.6 x10 47 N
35

36. 3 q3
q1 q C
C C q1= q3=5.0
q2= 2.0 C
a = 0.1 m
F31

F32 2
6 6
q2 q3 9 (2.0 10 )(5.0 10 )
F32 ke 2 (8.99 10 ) 2
9.0 N
a (0.1)
 q1 q3 (5.0 10 6 )(5.0 10 6 )
F31 ke (8.99 109 ) 2
11N
( 2a ) 2 2 (0.1)
F31x F31 cos 450 , F31 y F31 sin 450
F31 cos 450 F31 sin 450 11 2
2
7.9 N
F3 x F31x F32 7.9 N 9.0 N 1.1N
F3 y F31 y 7.9 N

F3 ( 1.1i 7.9j) N
36

37. 4 q1 470
1,2,4) q2
250 3,3,0)
q1 q2
 qq qq
ˆ
F = k  r = k 1 2
  rˆ
1 2
21
r
e
2 21
q q2  
e
r- r
2 21
21
F21 = ke  1  3 (r2 - r1 )
2 1
qq  r2 - r1 
= k   (r - 1 2
r)
 (9 x109 )(470 x10- 6 )(250 x10- 6 )(2iˆ + ˆ - 4kˆ)
e 3 2 1
r- r 2 1 j
   F21 =
ˆ + ˆ - 4k
r21 = r2 - r1 = 2i j ˆ 4.583

  2 1 2 j ˆ
F21 = 21.97iˆ + 10.99 ˆ - 43.94k N
r2 - r1 = = 2 + 1 + 4 = 4.58
37

38. Electric field
+ +
q3 F
Q
q1
+ +
q2
F F
Q
P ?

39. + +
q3 F
Q
Q
q1
+ +
q2
F F
?
?

40. ?
?
?
?

41. ?
+ + q0
q0 F
Q
+++
++++
++++
++++++ 
+ + + ++++ +
+++ + F
++++++ +++ lim
++++++++
q0 0 q0
++
++

42.  
E = F / q0



43. VS
Test charge
+
Source of Electric field
 
FE E

+ 
E

FE
-

- 
E 
FE
- 
E
- 
FE

44. 
 F
E lim
q0 0 q0
E = F / q0
kqq0 kq
E= 2 = 2
r q0 r
***
 
 F F
? E
q0 q0

45. ?
+q1
-q2
+q4
-q3
E20
qn
En0 P
E10
P (
     qi
EP E1 E2 ........ En Ei k ˆ
r
2 i
i i ri

46. •
•
– 
 dv y 1 
ay qE
dt m
•

47. 
47

48. (CRT)
• CRT
• CRT

49. •
Fe = qE = ma

a = qE /m

49

50. 5 9.6x10-14 kg
2x106 N/C

F 0
FE ( Fg ) 0
++++++++
FE Fg FE
qE mg
q 2 106 N / C 9.6 10 14
kg 10 m / s 2
19
q 4.8 10 C
Fg
E
FE E
- - - --19- - - - - -
-
- 4.8x10 C

51. Electric
ra a Q Q
+ Ea k 2 Eb k 2
rb ra rb
Q
b
Ea Eb
a b
?

52. Electric field lines



53. 
B

54. Electric field lines

55. Electric field lines
Electric

57. + -

58. ??????

59. ?
•

60. 6 q C
q - C x
m P
: P
, m
P 2
 q1 (7.0 10 6 )
E1 ke 2 (8.99 109 ) 3.9 105 N / C
r1 (0.40)2
 q2 (5.0 10 6 )
E2 ke 2 (8.99 109 ) 1.8 105 N / C
r2 (0.50)2
 
E1 3.9 10 j ; E2 1.1 105 i-1.4 105 j
5
   
E E1 E2 1.1 10 i+2.5 10 j E 2.7 105 N / C
5 5

61. 7 A
2 C q = C
+ q1 q1
A q0
3cm 3cm
+ A
4cm    
  E1 E E1 E2
- q2 2
E E
2 C E1 ˆ
E1 cos i E1 sin ˆ
j
y E2 ˆ
E2 cos i E2 sin ˆ
j

E2 cos q1 =q2 r1= r2 E1=E2
+  x 
ˆ
  q0 E1 cos E 2 E1 sin j
E2 E2 sin    kQ  kq1
E1 sin E1 E 2
ˆ
r EA 2 2
sin ˆ
j
r r1
 9 109 2 10 6 3ˆ N
4 3 E 2 i 0.86 10 7
cos และsin
5 5 (5 10 2 ) 2 5 C

62. y
8 q1= q2 = q3
+q1
a a
+q2
q
a a 2 
E3 a
q3
   
x E0 E1 E2 E3
a  
E2 E1 q2 = q3
 
r2=r3
+q3
E0 E1
 
E1 cos E0 E1 cos i E1 sin ˆ
ˆ j
 kQ


E1 E 2
rˆ
E2 sin r
 kq1
a 2 1 E0 cos i ˆ kq1 sin ˆ j
a sin
2 
2
r1 kq r12
kq1 ˆ
1 E0 1 ˆ
i j
a และ
cos 2 2a 2
2 2a 2
2

63. • : ,
• :
E
E
•
kq
E= 2
r

64. 1.
dq dE

65.  dqi
 qi dE ke 2
Ei ke 2 ri
r
 
i   dq
E Ei E dE ke 2
r
i

66. 9 l Q
P
d
dx
dq
dE
dq
dE k 2
x
Q
dq dx dx
l

67. P
dE
ke dq
dE
EX dE dE
x2
l d l d
ke dx
2
dx ke
d
x d
x2
l d
1 1 1 ke l
ke ke
x d l d d d (d l )

68. (linear charge dens
 Q
Q dq

 d d
dq d dq

69. (area charge density)
A
Q dA
Q dq
A dA dq
dq dA

70. (volume
charge density) :
V
Q
dV
Q dq
V dV
dq
dq dV

71. 10
a +Q
x
+Q
a
x Q ds
s
ds
Q Q
s
+Q
Q dq
l º =
s ds

72. ds Q
dq ds ds
s
dq
dq2 dq1 =
dq1
 y
 
dE2 E2 sin E2

x  +
E2 cos
x

dE1 q0 E1 cos
 
dq2 E1 sin E1

73. Ex
= ò dE
dq dE = dE cos q
a
r a2 x2
 E= ò dE cos q (1
dE cos )
x  dE =
kdq
dE r2
Q
k dq x kQ x
dE cosq E= ò 2 = 2
0 (a + x ) a + x (a + x2 ) a 2 + x2
2 2 2
kQ x
E
(a 2 x 2 ) a 2 x 2
x a
x kQ
cos E 2 2 3
x
a2 x2 (a x ) 2

74. (Electric Flux)
?
 :
 E =EA

75. (Electric Flux)

E EAcos
E EA = 0o
E
0 = 90o

76. C
E
q 1 10 6 3
E kE 2 (9 109 ) 899 10N/C
.
r (1) 2
E EA 3
(8.99 10 )(12 .6) 1.13 10 5 N m 2 /C
. . = 4p r 2 = 4(3.14)1 = 12.6 m2

77. ( )
•
 
E Ei Ai cos i Ei Ai
•    
E
lim Ei . Ai E.dA
Ai 0
i

78. Close surface



79. • (1), ;θ
<90o, Φ
• (2),
; θ =90o, Φ = 0
• (3), E EAcos ;90o

80. ( )
   
E
lim Ei . Ai E.dA
Ai 0
i
 
E E dA E n dA
En


81. Flux through a cube
E
x
L
E dA
A=L
L
L
 
E dA E(cos1800 )dA E dA EA EL2
1 1 1
 
E dA E(cos 00 )dA E dA EA EL2
x 2 2 2
E EL2 EL2 0 0 0 0 0

82.    
E
lim Ei . Ai E.dA
Ai 0
i surface
?
 ?
 ?

83. Gauss’ Law
 Gauss’ Law
E
0
  qin
E E.dA
surface 0


0 = (permittivity of free space

84.  E
 
E E dA
  qin
 E E dA
ε0
• qin E

84

85.  q
r
E=keq/r2
***
Gaussian surface ( 85

86. •


surface integral)
86

87. (Point Charge)
  qin
E
E.dA Gauss’ law
surface 0

88. q
S1 S2
S3
q/ 0 S1
S1
q
S2 , S3
q/ 0 88

89. 89

90. q
•
q

q
  qin
E E dA EdA
εo
qin
Ñ
E ò dA =
e0
q q q
E 4πr 2
E= = ke 2
ε0 4πεo r 2
r 90

91. Q
a r>a r<a
r>a r
  qin
E E dA EdA
εo
qin
E dA
εo
Q
E 4πr 2
=
εo
Q
E=
4πεo r 2 91

92. r<a r
 qin < Q
Q qin
4 / 3 a3 4 / 3 r3
3
qin Q r/a

  qin
E E dA EdA
εo
3
Q r/a
 E 4 r2
0
3
Q r /a Q
E= = ke 3 r
4πεo r 2 a
92

93.   qin
E E dA EdA
εo
λl
E 2πrl =
εo
λ λ
E= = 2ke
2πεo r r

93

94. •
•
•
q2EA
in σA σ
2EA = 2EA = E=
εo εo 2ε o
94

95. (Su
E
2 0
σ
(Area charge density)

96. q
R R
E
(r>R)
 
E dA EdA
qin
εo
q 1 q
E 4πr 2
E , r R
ε0 4πε0 r 2
 
(r<R) dA
E E 4πr 2 0
ε0
E 0, r R
96

97. - E
-
AE EA cos
 
- E E dA
surface
-
E
0   q in
E E dA
0 97

98. R Q kEQ/r2
kEQr/R3
R kEQ/r2
Q 0 r<R
2k E / r
/2 0
/ 0
0
98

99. q 5 C
q -8 C q q2
P
2
q3 q2 q1 q
C C q1=
q3=2.0 q2= 3.0 a=1m

100. http://www.rit.ac.th/homepage-sc/charud/selftest/2/index2
1. q1 = q
q2 = q5 = -5.9 nC q3 = -3.1 nC
100

101. http://www.rit.ac.th/homepage-sc/charud/selftest/2/index2
2.
3, 4, 2, 1
101

102. http://www.physics.sci.rit.ac.th/charud/oldnews/48/magnetic/OnlineTest_V4/inde
http://www.rit.ac.th/homepage-sc/charud/selftest/2/index
102

103. 2.
?
 …..

?

104. Wg Ug
m

105. A B
r

106. ? r
 
D U = - ò F .ds
q0E
Test charge
q kq
E = k 2 , D U = - q0 ò 2 .dr
r r
qq0 qq0
UB UA k k
rB rA
q2 q1
( U (r ) k
r
q2 q1
( U (r ) ) k
r

107. ?
q2 q1 Gm1m2
U e (r ) k U g (r )
r r



G
(universal gravitational 6.67259 x 10-11
G=
constant) N.m2 / kg2

108. Qq
U e (r ) k
+10 μC r
r +10 μC
+20 μC
+Q r
+20 μC U e (r ) Q
k Const
q r
Q r
U e (r )
Equipotential line V (r )
q

109. q0E V VB VA
U We Wext
q0 q0 q0
Test charge V
Qq0
Fext Fe q0 E k 2
r
kQ kQ
VB V A
rB rA
:
+1 C
kQ
V (r )
r

110. ?


U We Wext
V VB VA
q0 q0 q0

111. •
(equipotential surface)
 B
A
C
 B B C

111

112. •


112

113. •

1 1
A B B -VA = keq r - r
V
B A

V =0 rA =
q
V = ke
r
 1/r 113

114. •
qi
V = ke
i ri
V=0 r=∞


114

115. U q0 Ed
U q0 Ed
V Ed
q0 q0
115

116. Ex. V
-Q
+Q 3
+Q a +Q V k
qi
ri
P 2Q 2Q 2Q 2Q
a a
k
2
a a a a
+Q -Q 2 2kQ
a

117. Ex 9 (i) P
(ii)
P

118. • dq
dq
dV = ke
r

dq
V = ke
r
 V=0
118

119. • Q
a P
x
dq λdl
dV = ke ke
r r
dq dl
V = ke ke λ
r x 2 a2
2πa keQ
V = ke λ
x2 a2 x2 a2
Q dq
 d 119

120. L
[C/m] P
d [m]
x
dx P
L d
kdq k dx dq = dx
dV
r d x
L
k dx L d L
V dV k ln( d x) 0 k ln( )
0
( d x) d

121. Q q
R r
q1 q2 Q R
V ke ke 1
r1 r2 q r
121

122. Q q
E1 ke 2 E2 ke
R r2
QE R
1/E2
q r
Q
E1 kQ / R 2 R2 Q r2 Rr 2 r R
E2 kq / r 2 q qR 2 rR 2 R E2 E1
r2
r
122

123. 


A
E ds 0 B)E
 ds


123

124. E V

q
 V = ke
r

q
E ke 2
r
124

125. •
q1 q2
U = ke
r12


125

126. 
q1q2 q1q3 q2 q3
U = ke + +
r12 r13 r23
126

127. Ex. q1=2.0 µC
XY q2=-6.0 µC
ก) m
P m
ข)
μC q3=3.0
P
ค)
127

128. qi q1 q2
V ke ke
ri r1 r2
9 2 2 2.0 x10 6 C 6.0 x10 6 C
Vp 8.99 x10 N m / C
4.0 m 5.0 m
6.29 x103 V
U U f Ui
Ui 0  ri Uf q3V p
U q3Vp 0 3.0 x10 6 C 6.29x103V 0
2
1.89 x10 J
128

129. q1q2 q1q3 q2 q3
U ke
r12 r13 r23
2.0 x10 6 C 6.0 x10 6 C
8.99 x109 N m2 / C 2
3.0 m
2.0 x10 6 C 3.0 x10 6 C 3.0 x10 6 C 6.0 x10 6 C
4.0 m 5.0 m
2
5.48 x10 J
129

130. 3.
•
 (Capacitor)
capacitance)

130

131. Capacitor
131

132. •


132

133. 
Q
C=
ΔV
(farad, F)
133

135. •


135

136. 



Q Q Q εo A
C= = = =
ΔV Ed Q/εo A d d
136

138. •
a q
E
2 b 0 Lr
q b
V ln
2 0L a

Q = L L
2πε
C= 2k ln b / a
0
b
ΔV e
ln
a
138

140. •
a

b 1 1
ΔV = keQ -
b a

Q ab ab
C= = 4πε0
ΔV ke b - a b a
 b
ab a
C= 4πε0a
ke b ke
140

141. b
a
r

142. • C = a/k a
•
•

143. •



143

144. 
Qtotal= Q1+Q2=C1V+C2V



Ceq V=C1V C2V
Ceq =C1 C2 144

145. •
 C1
C2
C2

C2
C2

C1
-Q 145

146. 

 Q Q1 Q2
V V1 V2 ...
Q Q1 Q2 1 1 1
= + = + …
Ceq C1 C2 C C1 C2
146

150. •
q
dW = ΔVdq = dq
C
Q q Q2
 W=
0 C
dq =
2C

Q2 1 1
U= = QΔV = C(ΔV)2
2C 2 2

150

151. •
1 1 eA
U CV 2 ( o Ad ) E 2 C= 0
,V = Ed
2 2 d

U 1
uE o E2
Ad 2

151

152. •

C kCo k o A/ d

k

152

153. 153

154. 7.60 cm2
1.8 mm
ก) 20 V
ข)
ค)
ง)
A=7.60 cm2 , d=1.8
V Ed V=20 V
mm, E V 20V
จ) d 1.8 x10 3 m
11.1x103 V / m 11.1 kV / m
154

155. E 0E 8.85x10 12 C 2 / N m2 11.1x103 V / m
0
9
98.3x10 C / m2 98.3 nC / m2
A 7.6 x10 4 m2
C 0 8.85x10 12 C 2 / N m2
d 1.8x10 3 m
3.74 x1012 F 3.74 pF
Q
C Q CV 3.74 x1012 F 20 V
V
74.7 pC
1 1 12 2
U CV 2 74.7 x10 C 20 V
2 2
14.9 x10 9 J 14.9 nJ
155

156. F
10
A
10 F
B
A 10 F B
10 F
C C1 C2 C3
10 F 10 F 10 F
30 F
156

157. 3
18V
a a c
C1
C3=20µF b
C1=15µF C1=15µF
18 V C2=10µF
C2=10µF C3=20µF
18 V
• C2 C3
Ccb C2 C3 10 F 20 F 30 F
• c b a
b a +Q -Q +Q -Q b +Q -Q
C1=15µF C ab C
18 V
157
18 V

158. •
a 1
b 1 1 Ccb C1
Cab C1 Ccb C1Ccb
C1Ccb 15 F 30 F
Cab
Ccb C1 30 F 15 F
15 30
F 10 F
45
•
Q Q
Q
C Q CV 10 F 18 V 180 C
V
158

159. …The
End…