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### 1 ไฟฟ้าสถิตย์ physics4

1. 1. 432204 AJ. Suminya Teeta Faculty of Science Technology Rajabhat Maharakham University (RMU)
2. 2. Electrostatics)1.2.3.
3. 3. 1.      3
4. 4. . » » » »3. » »
5. 5. Electrostatics : ( Electric Current) : IAmpere AMP. Amp.Meter Direct Current):
6. 6. 1 2. 3. 4. 5. ……………
7. 7. ? Thales of Miletus (600 BC) : http://faculty-staff.ou.edu/
8. 8. Benjamin Franklin (1706 -1790) ?( ) (fluid) : http en wikipedi
9. 9. :(Static Electric)
10. 10. • ???????•••
11. 11.  -
12. 12. (Electric Charges)•• C : C x1018 A s 12
13. 13. •••  
14. 14. •  15
15. 15. - ++ - - +
16. 16.  e  q=  N Ne  e = 1.6 x 10-19  C = -e q  q = +e 17
17. 17.     18
18. 18. ????????• ??????????
19. 19. ????1.2.3.**** polarization
20. 20. 1.• 2• 2
21. 21. 2.••
22. 22. 3. ( Induction) •
23. 23. ???••
24. 24. (Coulombs Law• Charles Coulomb Fe q1q2 1 Fe r2 25
25. 25. (Coulomb La r q1 q 2q2 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) =
26. 26.  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 F21q q q q qq q q 27
27. 27.  q1q 2  q 2q1 F12 = ke 2 r12ˆ F21 k E 2 r21ˆ r rF12 q2 q1ˆr12 q1F21 q2 q1ˆr21 q1 q2 q2 (Repulsive force) q1 q2 (Attractive force)     F F F12 F21 12 21 q1 q2 q1 q2 r r 28
28. 28. q q3 q2 q32- - + +ˆr ˆ r ˆ r r r r  = +q1 - F - 13 q1 q1 -   F1 F12 q1 29
29. 29.    r = r- r 12  1 2   r- r z ˆ r =  12 1 2  F12 r- 1 r q1  q1 q 2 q q2 r1F12 = 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 q2F21 = ke  2 r ˆ21 = ke  1  2 r21 ˆ r21 r2 - r1 x q1 q 2   = ke   3 (r2 - r1 ) r2 - r1
30. 30. q1 q2 q3   q3 q1 q2F31 F32 q1    F3 F31 F32 - r31 ˆ r31  q3q1 F31 ˆ r31  q2q3 F32 4 2 r31 - ˆ r32 0 r32 +F31  F32 q3q 2 ˆ r32 2 4 r32  0 F3 31
31. 31. 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 qiFij qi qjˆrij (unit vector) qjrij qi qj qi , qj (C) rij (m) Fi , Fij (N) 32
32. 32. 1 1.0 1.0 KQ1Q2F r2 9.0 109 Nm 2 / C 2 1.0 C 1.0 C 2 (1.0 m) 9.0 109 N 1C
33. 33. 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
34. 34. 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 kgFg 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
35. 35. 3 q3 q1 q C C C q1= q3=5.0q2= 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
36. 36. 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 - 4kr21 = 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
37. 37. Electric field + + q3 F Q q1 + + q2 F F Q P ?
38. 38. + + q3 F Q Qq1 + + q2F F ? ?
39. 39. ?? ? ?
40. 40. ?+ + q0 q0 FQ +++ ++++ ++++ ++++++ + + + ++++ + +++ + F++++++ +++ lim ++++++++ q0 0 q0 ++ ++
41. 41.  E = F / q0
42. 42. VS Test charge +Source of Electric field   FE E  +  E  FE -  -  E  FE -  E -  FE
43. 43.   F E lim q0 0 q0 E = F / q0 kqq0 kq E= 2 = 2 r q0 r***    F F ? E q0 q0
44. 44. ? +q1 -q2 +q4 -q3 E20 qn En0 P E10 P (     qiEP E1 E2 ........ En Ei k ˆ r 2 i i i ri
45. 45. •• –   dv y 1  ay qE dt m•
46. 46.  47
47. 47. (CRT)• CRT• CRT
48. 48. • Fe = qE = ma a = qE /m 49
49. 49. 5 9.6x10-14 kg 2x106 N/C  F 0FE ( Fg ) 0 ++++++++FE Fg FEqE mgq 2 106 N / C 9.6 10 14 kg 10 m / s 2 19q 4.8 10 C Fg E FE E - - - --19- - - - - - - - 4.8x10 C
50. 50. Electric ra a Q Q+ Ea k 2 Eb k 2 rb ra rbQ b Ea Eb a b ?
51. 51. Electric field lines
52. 52.  B
53. 53. Electric field lines
54. 54. Electric field lines Electric
55. 55. + -
56. 56. ??????
57. 57. ?•
58. 58. 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
59. 59. 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 jE2 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
60. 60. 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 ja sin 2  2 r1 kq r12 kq1 ˆ 1 E0 1 ˆ i j a และ cos 2 2a 2 2 2a 2 2
61. 61. • : ,• : E E• kq E= 2 r
62. 62. 1.dq dE
63. 63.  dqi qi dE ke 2Ei ke 2 ri r  i   dqE Ei E dE ke 2 r i
64. 64. 9 l Q P ddx dq dE dq dE k 2 x Qdq dx dx l
65. 65. 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 )
66. 66. (linear charge dens Q Q dq   d d dq d dq
67. 67. (area charge density) AQ dA Q dq A dA dq dq dA
68. 68. (volumecharge density) : V Q dV Q dq V dV dq dq dV
69. 69. 10 a +Q x +Qa x Q ds s ds Q Q s +Q Q dq l º = s ds
70. 70. 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
71. 71. 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 kQcos E 2 2 3 x a2 x2 (a x ) 2
72. 72. (Electric Flux) ?  :  E =EA
73. 73. (Electric Flux) E EAcosE EA = 0o E 0 = 90o
74. 74. 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
75. 75. ( )•   E Ei Ai cos i Ei Ai•     E lim Ei . Ai E.dA Ai 0 i
76. 76. Close surface
77. 77. • (1), ;θ <90o, Φ• (2), ; θ =90o, Φ = 0• (3), E EAcos ;90o
78. 78. ( )     E lim Ei . Ai E.dA Ai 0 i   E E dA E n dA En
79. 79. Flux through a cube E x L E dA A=LL 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
80. 80.     E lim Ei . Ai E.dA Ai 0 i surface ?  ? ?
81. 81. Gauss’ Law Gauss’ Law E 0   qin E E.dA surface 0 0 = (permittivity of free space
82. 82.  E   E E dA   qin E E dA ε0• qin E 84
83. 83.  q r E=keq/r2 *** Gaussian surface ( 85
84. 84. • surface integral) 86
85. 85. (Point Charge)   qin E E.dA Gauss’ law surface 0
86. 86. q S1 S2S3 q/ 0 S1 S1 q S2 , S3 q/ 0 88
87. 87. 89
88. 88. 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
89. 89. Qa r>a r<a r>a r   qinE E dA EdA εo qin E dA εo Q E 4πr 2 = εo Q E= 4πεo r 2 91
90. 90. 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
91. 91.   qin E E dA EdA εo λl E 2πrl = εo λ λ E= = 2ke 2πεo r r 93
92. 92. ••• q2EA in σA σ 2EA = 2EA = E= εo εo 2ε o 94
93. 93. (Su E 2 0σ (Area charge density)
94. 94. q R RE (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
95. 95. - E- AE EA cos  - E E dA surface- E 0   q in E E dA 0 97
96. 96. R Q kEQ/r2 kEQr/R3 R kEQ/r2Q 0 r<R 2k E / r /2 0 / 0 0 98
97. 97. q 5 C q -8 C q q2 P 2q3 q2 q1 q C C q1=q3=2.0 q2= 3.0 a=1m
98. 98. http://www.rit.ac.th/homepage-sc/charud/selftest/2/index21. q1 = q q2 = q5 = -5.9 nC q3 = -3.1 nC 100
99. 99. http://www.rit.ac.th/homepage-sc/charud/selftest/2/index22. 3, 4, 2, 1 101
100. 100. http://www.physics.sci.rit.ac.th/charud/oldnews/48/magnetic/OnlineTest_V4/indehttp://www.rit.ac.th/homepage-sc/charud/selftest/2/index 102
101. 101. 2. ? ….. ?
102. 102. Wg Ug m
103. 103. A B r
104. 104. ? r   D U = - ò F .ds q0ETest 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
105. 105. ? 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
106. 106. 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
107. 107. q0E V VB VA U We Wext q0 q0 q0Test charge V Qq0 Fext Fe q0 E k 2 r kQ kQ VB V A rB rA : +1 C kQ V (r ) r
108. 108. ? U We Wext V VB VA q0 q0 q0
109. 109. • (equipotential surface) B A C B B C 111
110. 110. •   112
111. 111. • 1 1 A B B -VA = keq r - r V B A V =0 rA = q V = ke r 1/r 113
112. 112. • qi V = ke i ri V=0 r=∞ 114
113. 113. U q0 Ed U q0 EdV Ed q0 q0 115
114. 114. 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
115. 115. Ex 9 (i) P (ii)P
116. 116. • dq dq dV = ke r dq V = ke r V=0 118
117. 117. • Q a P x dq λdldV = 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
118. 118. L [C/m] P d [m] x dx P L d kdq k dx dq = dxdV r d x L k dx L d LV dV k ln( d x) 0 k ln( ) 0 ( d x) d
119. 119. Q qR r q1 q2 Q R V ke ke 1 r1 r2 q r 121
120. 120. Q q E1 ke 2 E2 ke R r2 QE R 1/E2 q r QE1 kQ / R 2 R2 Q r2 Rr 2 r RE2 kq / r 2 q qR 2 rR 2 R E2 E1 r2 r 122
121. 121.  A E ds 0 B)E  ds 123
122. 122. E V q  V = ke r q E ke 2 r 124
123. 123. • q1 q2 U = ke r12 125
124. 124.  q1q2 q1q3 q2 q3U = ke + + r12 r13 r23 126
125. 125. Ex. q1=2.0 µC XY q2=-6.0 µC ก) m P m ข) μC q3=3.0 P ค) 127
126. 126. qi q1 q2 V ke ke ri r1 r2 9 2 2 2.0 x10 6 C 6.0 x10 6 CVp 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
127. 127. q1q2 q1q3 q2 q3U 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
128. 128. 3.• (Capacitor) capacitance) 130
129. 129. Capacitor 131
130. 130. • 132
131. 131.  Q C= ΔV (farad, F) 133
132. 132. • 135
133. 133.  Q Q Q εo A C= = = = ΔV Ed Q/εo A d d 136
134. 134. • 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
135. 135. • 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
136. 136. b ar
137. 137. • C = a/k a••
138. 138. • 143
139. 139.  Qtotal= Q1+Q2=C1V+C2V Ceq V=C1V C2V Ceq =C1 C2 144
140. 140. • C1 C2 C2 C2 C2 C1 -Q 145
141. 141.  Q Q1 Q2 V V1 V2 ... Q Q1 Q2 1 1 1 = + = + … Ceq C1 C2 C C1 C2 146
142. 142. • 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
143. 143. • 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
144. 144. • C kCo k o A/ d k 152
145. 145. 153
146. 146. 7.60 cm2 1.8 mm ก) 20 V ข) ค) ง) A=7.60 cm2 , d=1.8V Ed V=20 Vmm, E V 20V จ) d 1.8 x10 3 m 11.1x103 V / m 11.1 kV / m 154
147. 147. 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 m2C 0 8.85x10 12 C 2 / N m2 d 1.8x10 3 m 3.74 x1012 F 3.74 pF QC 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
148. 148. F 10 A 10 F B A 10 F B 10 FC C1 C2 C3 10 F 10 F 10 F 30 F 156
149. 149. 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
150. 150. • 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
151. 151. …TheEnd…
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