36
m²s¥¥~ Êj× Ój¥¢Ô~צ¥m§§ s®jË ¥Ó ¥ s§p q² Ój~ j¥jjq¡©Ï jwkpm¢× ©Ï j×©Ï ~¥j¬q¡ j¡j~רsÔ©Ï~¨s~q² ¥¬j~ jwkp§× ¦Ópj²¥}©Ï pq©Ï¨Ô pp ¦pp}¦ §}q}j¥j¨Ôj¥©}Ôj mÔmÔ ²m¢ Ô©}Ô©¡j~רsÔ¨s~q²mm¢ Ó©jm¡| ¦q ¦m¡|j|ppm× ©}Ô¦jÓ j¨sÔjjp~× ¦q~~רj¥ Ô¦j¦jÔÙv mm m}s Ô®p~jÓ~× ¥m§§ ¦p¦}Ô m¥jkÔp×j j¥¢Ô }p¦j²~¡¥Ûjpp©Ï¨Ôq¡©Ï§}jk}j¦j¥²©Ï~ ¦m²|¦p©Ï~jwkpm¢× ¦m²|©Ï¦¦p©Ïj²j¡mq¡©Ï¢ Ó¨©Ï ®p©Ï ×¥pqjq¡}q¡§}j¦¥j¥~× ¦m²|ppj×©Ï ©Ï ¦m~Ópj×Ópp~²¦Óp¨}« Ójkp~¥j¬q¡ m×Ópq¡©Ï m~Ópj× ¦mq¡kp~¥j¬q¡ ¦pp¨~¥j¬q¡ ¦mq¡¢ ®pm²||~Óp« ¥jkÔp ²m¢Ô¥p©Ï~©jj²pkp¥mp¨sÔ©Ïps} ¦jxj|רs~q² j¥mkp¥¬j~¦j¦©Ï¨}~² m×Ópj¦©Ï¨}~² jm¥¬¥kp¥¬j~ m¦Ókp¥¬j~¨}~²¦® Ô~}kp}~² ¦m²||~Óp« ¥jkÔp jwkp§× m×Ópm~Ôjm ®Ô~} ¦~Ôkp~²§ ¡|¢mp~ ¦m²||~Óp« ¥jkÔp ®p¦m²|m~Ô¢¥²~~Ô ~Ój¦¡j¦¦k }p ¦m²|¥¬¥kp¦Ópj²¥}©Ïj¦~p ®p¦m²|pp©Ï ¦j²p©Ï }p¦m²|¥¬¥¢qjj~Ó¦~¥~¦¡j¦¦k ®pm²||~Óp« ¥jkÔp¨pq©Ïj¦~ptpj}Ô¦~¥~¦m~Ô pp}¦¥Ûpp©Ï ®p mÔ¦¥j j¥m§§« ²¦jÔÙv ~pm~Ôpjp}Ôpp©Ï ®p} j¥¢Ô úèĀÖùĆüċòĄñèòāñöăÙāċíăēðċäăðöăæñā÷āùäòŞČôÿċæÓčèčôñĄ äāðëôÐāòċòĄñèòĈś ÐôćŚðùāòÿÐāòċòĄñèòĈśöăæñā÷āùäòŞČôÿċæÓčèčôñĄ ØéĀéêòĀéêòćÖ í÷ äāðúôĀÐùĈäòČÐèÐôāÖÐāò÷ąÐøāÑĀĔèíĆĔèßāè íćæç÷ĀÐòāÙ ALV$L ÙĀĔèðĀçñð÷ąÐøāêŒæĄē ċôŚð êćŚĊñăðèĊñăðÕ õññ÷ïó ĊøçĀþÒėĀ êćŚãñõÖ êöïĀóă øĆåæĂČûîĀø ñöïĀçÿø ïÕÒóøĆÐ êöéñăâĀ ĊìØñïăöñă èññáĀæĂÏĀñ ö âñìĂĊØ÷Þŝ óĂēïøĆõññá

Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

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Page 1: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2
Page 2: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

www.MACeducation.com

I

Page 3: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

“Physics M.5 Vol.2”

Page 4: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2
Page 5: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

1123

456

1. 2. 3.

4. 5.

6.

Page 6: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

31

(electrostatics)

(Thales of Miletus)

2087 (William Gilbert)

1

(atom) 3

(proton) (neutron) (electron)

(nucleus)

1.1

2 1.1

Page 7: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

4

3 1.1

1.1

p n e

(�)

(�)

�e: (�1.602�10�19

C) 0

�e: (�1.602�10�19

C)

1.67262�10�27

kg 1.67429�10

�27 kg

9.10�10�31

kg

(law of conservation of charge)

1 1

2 2 2

1. 2

51

1.2

� � �

1.1

1 1 2 1 3 2

1 1 1-2

2

3 1-2

Page 8: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

6

1.1

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18

1.3

1.

2 3

1.3

71

2.

- -

-

1.4

3. (C) (A B) C C

1.5

1.5

A B

A

B

A B

A

B

A B

A

B

A

C

BAB

Page 9: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

8

1.5 A B C A C B

C A B B

A B

1 6

1.6

1 (electroscope)

1 1 7 2 A

1 7

A

B

B

A

A

B

A B

91

3 1 7

4 1 7 5 A

1 7

A

1.7

A A

2 1. (pith-ball electroscope)

1 8

1.8

A A A

A

Page 10: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

10

1.9

1.9

2. (leaf electroscope)

2 1 10

1 11

1.11

B B

� �� �

� �� �

� �� �

��

��

���

A

1.10

111

1 12

1.12

1.1

B �

B B

B �

Page 11: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

12

1.2

1 2

3

4 5

1 2 3 4 5

1. 2. 3. 4. 5.

131

- (Charles-Augustin

de Coulomb)

(electric force : FE)

2

1 2

3

1.13

2

F � kq1 q2

r2

r

F21�q1

F21 �q1

F21 �q1

F12 �q2

F12�q2

F12�q2

Page 12: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

14

F � q1q2

F � 1

r2

q1 q2 r

F � kq1q2

r2

(1.1)

F q1 q2 (N)

q1 q2 (C)

r (m)

k 9 � 109 2

/C2 1

4 �0 �0

(permittivity) 8.854 � 10�12 2

/C2

(1.1) 1

1.3 2 q1 �5 q2 �10

q3 2 a 0.2 q3

q1 � �5 �C, q2 � �10 �C, q3 �

2 �C a � 0.2 nm

q3 q1 q2 q3

F � kq1q2

r2

�q1 �q3 F31

F32

a

a �q2

F31�q3

F32

151

q1 q3

F31 � kq1q3

r213

� (9�109)(5�10

�6)(2�10

�6)

(0.2�10�9

)2

� 2.25�1018

N

q2 q3

F23 � kq2q3

r223

� (9 � 109)(10 � 10

�6)(2 � 10

�6)

(0.2 � 10�9

)2

� 4.5�1018 N

q3 F13 F23

F23 � F

213�F

223

F23 � (2.25�10

18)2�(4.5�10

18)2

F23 � 25.31�10

36

F3 � 25.31�1036 � 5.03�10

18

q3 5.03�1018

1.4 0.53�10

�18

qe � qp � e

FE � kqeqp

r2

FE � ke2

r2 …..(1)

FG � Gmemp

r2

…..(2)

Page 13: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

16

(1) (2) FE

FG �

ke2

r2

r2

Gmemp

FE

FG �

ke2

Gmemp

FE

FG �

(9 � 109)(1.6 � 10

�19)2

(6.67 � 10�11

)(9.1 � 10�31

)(1.67 � 10�27

)

FE

FG � 2.27�10

39

2.27 � 10

39

1.5 �q, �q �2q 0, 50 100 50

F � kq1q2

r2

A B

FAB � k(q)(q)

(0.5)2

FAB � kq2

0.25

B C

FBC � k(q)(2q)

(0.5)2

FBC � 2kq2

0.25

B FB � FBC �(�FAB)

FB � 2kq2

0.25 �

kq2

0.25 �

kq2

0.25

FB � 4kq2

N

50 4kq2 C

�q �qFCB FAB �2q

0A

50 cmB

100 cmC

171

1.6 A, B C A 1 � 10�6

A B –1 � 10�6 C AB � AC � 3

A

F � kq1q2

r2

A B

FAB � (9�10

9)(1�10

�6)(1�10

�6)

(3�10�2

)2

FAB � 10 N

A C

FAC � (9�10

9)(1�10

�6)(1�10

�6)

(3�10�2

)2

FAC � 10 N

A FA � FAB2

� FAC2

FA � 102 � 10

2

FA � 10 2 N

A 10 2

FAB

FAC

FA

�1�10�6

C

3 cm

3 cm

�1�10�6

CB

A

C

�1�10�6

C

Page 14: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

18

1.7 ABC �4�10�4 �4�10

�4 A B �1.6�10

�18 C C

F � kq1q2

r2

C A

FAC � (9�10

9)(4�10

�4)(1.6�10

�18)

(3�10�2

)2

FAC � 6.4�10�9 N

C B

FBC � (9�10

9)(4�10

�4)(1.6�10

�18)

(3�10�2

)2

FBC � 6.4�10�9 N

C

FC � FAC2

� FBC2

� 2FACFBC cos

FC � (6.4�10�9

)2 � (6.4�10

�9)2 � 2(6.4�10

�9)(6.4�10

�9) cos120º

FC � 6.4�10�9 N

C 6.4�10�9

FBC

FAC

FC

�4�10�4

C 3 cm �4�10�4

C

�1.6�10�18

C

BA

C

60º

60º 60º

191

E)

1. 2. k 3.

12

3

4

5

14Q

d

d

12Q 1Q

E �kQ

r2

E �V

d

Page 15: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

20

1

1.14

1.14

1

E �Fq (1.2)

q +1 Q (1.1)

F �kQ(1)

r2

F �kQ

r2

(1.2)

E �kQ

r2 (1.3)

� �

E �Fq

E �kQ

r2

211

1.2

1. - - -

2. 3. 4. 5. 6.

1.

2.

3-5

3. 4. 5. 1-4

1.

2.

3.

Page 16: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

22

1.2

1.15

1.15

1.

2.

3.

1.16

1.16 2

231

1.8 5.0�10�15

1.602�10�19

C F � 5�10�15

N

E �Fq

� 5�10

�15

1.602�10�19

� 3.12�104 N/C

3.12�104

1.9 A 6 10

E �kQ

r2

�(9�10

�15)(6�10

�6)

(10�10�2

)2

� 5.4�106 N/C

A 5.4�106

n q1, q2, ..., qn n

E � E1�E2�E3� �En (1.4)

1.10 q1 � q2 � �q q3� �2q (0,0), (2nm, 0) (2nm, 2nm)

(0, 2nm) q 1.6�10�16

r � 10 cm

Q � �6 CA

E

E � E1�E2�E3� �En

�q �q

�2qq3

q2q1

Page 17: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

24

E1 q1

E1 � kq1

r21

� (9�10

�15)(1.6�10

�6)

(2�10�9

)2

� 3.6�1011

N/C

E2 q2

E2 � kq2

r22

� (9�10

�15)(1.6�10

�6)

( 8 �10�9

)2

� 1.8�1011

N/C

E3 q3

E3 � kq3

r23

� k(2q)

r23

� (9�10

�15)(2)(1.6�10

�6)

(2�10�9

)2

� 7.2�1011

N/C

E1, E2 E3 x Ex � E3�E2 cos 45º

� (7.2�1011

)�(1.8�1011

) 22

� 5.9�1011

N/C

y Ey � E1�E2 sin 45º

� (3.6�1011

)�(1.8�1011

) 22

� 4.9�1011

N/C

E � Ex2 � Ey

2

� (5.9�1011

)2 � (4.9�10

11)2

� 58�1022 � 7.6�10

11 N/C

(0, 2nm) 7.6�1011

�q �q

�2q

2 nm

45º

2 nm

E3

E1E2

8 nm

q3

q2q1

251

1.11 A C q1 q2 3.6�10

�6 �1.2�10�6

AB 4.6 BC 1.8 B

EAB q1

EAB � kq1

r2AB

� (9�10

�15)(3.6�10

�6)

(4.6)2

� 1.5�103 N/C

q3

EBC � kq3

r2BC

� (9�10

�15)(1.2�10

�6)

(1.8)2

� 3.3�103 N/C

EAB EBC

E � EAB2

� EBC2

� (1.5�103)2 � (3.3�10

3)2

� 13�106 � 3.6�10

3 N/C

tan �

EBC

EAC �

3.3�103

1.5�103

tan � 2.2

� tan�1

(2.2) � 66º

B 3.6�103 66

EAB

q1 q2

q3

A

C

B

q1 � �3.6 C

q2 � �3.6 C

q3 � �1.2 C

A

C

1.8 mEBC

EAB

E

4.6 m

B

Page 18: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

26

(neutral point) 2

2

1. 1.17

1.17

2. 1.18

1.18 q1 q2

1.12 �2 �18 20

�q�q1 �q2

E2 E1

E2 E1�q1 �q2 �q

EB EA

20 cm

xA B

�2 C �18 CC

271

C

EA � EB

kqA

r2AC

� kqB

r2BC

qA

r2AC

� qB

r2BC

(2�10

�6)

x2

� (18�10

�6)

(20�x)2

(2�10�6

)(20�x)2 � (18�10

�6)x

2

(20�x)2 � 9x

2

20�x � 3x

x � 5 cm

�2 5

1.13 A B 0.3 A �1

B �0.25 B �0.25

B �0.25

C EA � EB

kqA

r2AC

� kqB

r2BC

qA

r2AC

� qB

r2BC

(1�10

�6)

(30�x)2

� (0.25�10

�6)

x2

(1�10�6

)x2 � (0.25�10

�6)(30�x)

2

x2 � (0.25)(30�x)

2

x � (0.5)(30�x)

1.5x � 15

x � 10 cm

A B B 10

30 cm

A BCEB EA

x

�0.25 C�1 C

Page 19: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

28

B �0.25

C

EA � EB

kqA

r2AC

� kqB

r2BC

qA

r2AC

� qB

r2BC

(1�10

�6)

(30�x)2

� (0.25�10

�6)

x2

(1�10�6

)x2 � (0.25�10

�6)(30�x)

2

x2 � (0.25)(30�x)

2

x � (0.5)(30�x)

0.5x � 15

x � 30 cm

A B B 30

1.2

1.19

30 cm

C

EB EA

x

�0.25 C�1 C

A B

291

1.19

q m E

qE

2 F � ma

qE � ma

a � qEm (1.5)

(1.5)

E � Vd (1.6)

V d

E

E

A

VA � 0

d

B

v

E�

�q

�qa

a

1.20

a � qEm

E �Vd

Page 20: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

30

1.14 1.6

F � 0

qE � meg

qV

d� meg

(1.6�10�19

) V

(1.6�10�2

)� (9.1�10

�31)(10)

V � 9.1�10�13

V

9.1�10�13

E e�

qE

meg

d �

1.6

cm

1. d0 E0 2 2d0

2. 3. 4. q1 � �2 q2 � �2 6

2 5. 2�10

�6 8�10�6

311

(electric potential : V) (J/C) (V)

V � kqr (1.7)

V Q (V)

k 9�109 2

/C2

q (C)

r (m)

�q E

qE B A 1.21

+q A

B B A

A B 1 A B

VB�VA � WA B

q (1.8)

1 1 2 1

V 5 kqr

2

V �kqr

E

F

B

A

qE

�q

1.21 A B

F VB�VA � WA B

q

Page 21: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

32

1 �q E �Q A

B 1.22

1.22 �q �Q

A B B A

VB�VA �kQrB

�kQrA

VB�VA � kQ 1rB

�1rB

A B A (VA � 0)

VB�0 � kQ 1rB

�1�

VB �kQrB

� W� B

q

V �kQr (1.9)

V Q (V)

k 9�109 2

/C2

Q (C)

r Q (m)

rB

rA

B

A

F�Q

�q

V �kQr

331

n

i�1Vi � V1�V2�V3�…�Vn (1.10)

q Q

U � kQq

r � qV (1.11)

U q (J)

r (m)

2 3

U � U12�U23�U31

U � kq1q2

r12�

kq2q3

r23�

kq3q1

r31 (1.12)

1.15 �2 �5 10

q � �2�10�6

C, Q � �5�10�6

C r � 10�10�2

m

VA �W� A

q

kQrA

�W� A

q

(9�10

9)(�5�10

�6)

(10�10�2

)�

W� A

(2�10�6

)

W� A � 0.9 J

0.9

n

i�1Vi � V1�V2�V3�…�Vn

U � kQq

r � qV

U � kq1q2

r12�

kq2q3

r23�

kq3q1

r31

10 cmA

�5 C

Q

�2 C

q

Page 22: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

34

1.16 ABC B BC 3 AB 4 10

�5 �0.6�10�5 A B

C

ABC AC

AC � AB2�BC

2

� 32�4

2 � 5 cm � 5�10

�2 m

A

VAC � kQA

rAC

� (9�10

9)(�10

�5)

(5�10�2

)

� �1.8�106 V

B

VBC � kQB

rBC

� (9�10

9)(�0.6�10

�5)

(3�10�2

)

� �1.8�106 V

C VC � VAC�VBC

� (�1.8�106)�(�1.8�10

6)

� 0 V

C 0

A

C

B4 cm

3 cm

10�5

C �0.6�10�5

C

351

1.17 A, B C 3.0�10�6

, 1.0�10�6

–1.0�10�6 AP 0.6 CP

0.3 BP 0.1 P

P VP � VA�VB�VC

� kQA

rA �

kQB

rB �

kQC

rC

� k QA

rA �

QB

rB �

QC

rC

� (9�109)

(�3�10�6

)

0.6 �

(�1�10�6

)

0.1 �

(�1�10�6

)

0.3

� 1.05�105 V

P 1.05�105

1.18 A, B C �2, �4 �6 P BC Q AB

QC b

2 � a

2�c

2�2ac cos �

QC2 � 60

2�25

2�2(60)(25)cos 53

QC2 � 2,419

QC � 49 cm

P VP � VA�VB�VC

� kQA

rA �

kQB

rB �

kQC

rC � k

QA

rA �

QB

rB �

QC

rC

A BP

C

50 cm

50 cm

A

P

Q

B C60 cm

2 C

�6 C�4 C

40 cm

49 cm

25 cm

25 cm

30 cm30 cm53º

2 CA

CBP�4 C �6 C

Q

Page 23: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

36

Q VQ � VA�VB�VC

� kQA

rA �

kQB

rB �

kQC

rC

� k QA

rA �

QB

rB �

QC

rC

� (9�109)

(�2�10�6

)

(25�10�2

) �

(�4�10�6

)

(25�10�2

) �

(�6�10�6

)

(49�10�2

)

� –1.82�105 V

P Q �2.25�105 –1.82�10

5

1.19 q1, q2, q3 q4 d q1 �12 q2 �24 q3 �31 q4 +17 d 1.3

P r

q1 q1q2 q2

q3 q3q4 q4

�d

d

p Pd d

� �

� �

d

r r

r r

d

d

d

P

q3 � �31 nC

q2 � �24 nC

q4 � �17 nC

q1 � �12 nC

371

r r � d2

2

� d2

2

� 2d

2

4

� 22

d � (0.7)(1.3) � 0.91 m

P VP � V1�V2�V3�V4

� kQ1

r � kQ2

r � kQ3

r � kQ4

r

� k Q1�Q2�Q3�Q4

r

� (9�109)

(�12�24�31�17)�10�9

0.91

� 356 V

356

U � U12�U13�U14�U23�U24�U34

� kq1q2

r12 �

kq1q3

r13 �

kq1q4

r14 �

kq2q3

r23 �

kq2q4

r24 �

kq3q4

r34

� k q1q2

r12 �

q1q3

r13 �

q1q4

r14 �

q2q3

r23 �

q2q4

r24 �

q3q4

r34

� k q1q2

d � q1q3

d �

q1q4

2r �

q2q3

2r �

q2q4

d �

q3q4

d

� (9�109) (12�10

�9)(�24�10

�9)

1.3 � (12�10

�9)(31�10

�9)

1.3

� (12�10�9

)(17�10�9

)

(2)(0.91) � (�24�10

�9)(31�10

�9)

(2)(0.91)

� (�24�10�9

)(17�10�9

)

1.3 � (31�10

�9)(17�10

�9)

1.3

� –1.24�10�6

J

–1.24�10�6

Page 24: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

38

�1

1.3

1.23 d

WAB � Fd

A B

VAB � VA�VB � WAB

q

VAB � Fdq �

(qE)dq

VAB � Ed (1.13)

1.23 B A +q A B

A B 1.24

A, B C B C

A BC

(equipotential

line) 1.25

1.23

E

F

B

d

A�q

VAB � Ed

1.24 A, B C

E

A C

B

d

S

391

1.25

1.20 2 20 500 10

15 2

E �d

�500

20�10�2

E � 2,500 V/m

2,500

E

E

E

�v

A B

d � 20 cm

V � 500 V

- -

Page 25: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

40

u � 0 a � 10

15 m/s

2

v2 � u

2�2aS

v2 � 0�2(10

15)(20�10

�2)

v2 � 4�10

14

v � 2�107 m/s

2�107

1.21 E 20 2�10

�9 A B C

A C WA C � q(VC�VA)

E � d

� VC�VA

d

VC�VA � Ed

WA C � q(Ed)

WA C � (2�10�9

)(20)(10�10�2

)

WA C � 4�10�9

J

4�10�9

(ds) A B V � � 0

(E�ds)

E

A

C

B

10 cm

10 cm

411

1.26

1.27

1.27

1.27

E

� �

� �

R R

E

V

R Rr r

Kq

r2

kq

R

kqr

Page 26: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

42

1.22 a 10 �1.6×10�6

5 10 14

5 cm

V � kQa

� (9�10

9)(�1.6�10

�6)

10�10�2

� �1.44�105 V

5 �1.44�10

5

10 cm

E � kQ

a2

� (9�10

9)(1.6�10

�6)

(10�10�2

)2

� 1.44�106 N/C

V � kQa

� (9�10

9)(�1.6�10

�6)

10�10�2

� 1.44�105 N/C

10 1.44�106

�1.44�105

14 cm

E � kQ

r2

� (9�10

9)(1.6�10

�6)

(14�10�2

)2

� 7.35�105 N/C

431

V �kQr

�(9�10

9)(�1.6�10

�6)

14�10�2

� �1.03�105 N/C

14 7.35�105

�1.03�105

1.23 10

10�9

1 B A

WBA B A

WB A � q(VA�VB)

� q kQrA

�kQrB

� kQq 1rA

�1rB

� (9�109)(10

�9)(1.6�10

�19)

10.2 �

10.5

� 4.32�10�18

J

1 B A 4.32�10�18

A

B50 cm

10 cm

20 cm

1. 2�10�4

5�10�2

2. Q 8�10�9 Q 10

3.

Page 27: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

44

�q

�q

(capacitor)

1.28

2

C � QV

451

d

1.29 d �Q �Q

1.29

2 1.

� �

2.

1(capacitance : C)

C � QV

(1.14)

C (F)

Q (C)

V (V)

C � QV

E

�Q

�Q

d

Page 28: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

46

a

V �kQa

QV

�ak

C �ak

(1.15)

t � 0

Q

2 V

W �12

QV (1.16)

U � 12

QV � 12

CV2 �

12

Q2

C (1.17)

1.24 C1 12 C1 250 C2 400 AB

C1

C2

AC C1

C2

AB C1 Q0

Q0 � C1V0

� (250�10�6

)(12)

� 3,000�10�6

C

U �12

Q0V0

�12

(3,000�10�6

)(12)

� 0.018 J

C �ak

W �12

QV

U � 12

QV � 12

CV2 �

12

Q2

C

C1

C2 C

A

B

� �

471

AC Q0 C1 C2

Q1 � C1V

Q2 � C2V

C1 C2 Q0 Q1�Q2 � Q0

V

V � Q0

C1�C2

� 3000�10

�6

(400�250)�10�6

� 4.6 V

C1

Q1 � C1V

� (250×10�6

)(4.62)

� 1.16×10�3

C

C1 1.16×10�3

C2

Q2 � C2V

� (400�10�6

)(4.62)

� 1.85�10�3

C

C2 1.84×10�3

C1

U1 � 12

Q1V1

� 12

(1.16�10�3

)(4.62)

� 2.68�10�3

J

C1 2.68�10�3

C2

U2 � 12

Q2V2

� 12

(1.85�10�3

)(4.62)

� 4.27�10�3

J

C1 4.27�10�3

Page 29: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

48

2

1. 1.30

1.30

1.30 2 V C1 Q1 C2 Q2

V1 � V2 � V

Q1 � C1V

Q2 � C2V

Q Q � Q1�Q2

Q � C1V�C2V

Q � (C1+C2)V

(1.14) QV

� C1�C2

C � C1�C2 (1.18)

n

C � C1�C2�C3�….�Cn

C1

C1

C1

V1 � V2 � VC � C1�C2

VV V

�� �

�� �

C2

C2Q2

Q1

C2 Cn

C � C1�C2

491

2. 1.31

1.31

V C1

( �Q) C2 ( �Q) V Q �Q C1 �Q

C1 Q �Q C2 �Q C2 Q

V V Q1 � Q2 � Q

V1 �QC1

V2 �QC2

V � V1�V2

V �QC1

�QC2

(1.14) QC

�QC1

�QC2

1C

�1

C1�

1C2

(1.19)

n 1C � 1

C1�

1C2

�1

C3�...�

1Cn

C2C1 Cn

C

��

�Q�Q

C1V1

�Q

�Q�Q �Q

V2

V V

C2

1C

�1

C1�

1C2

Page 30: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

50

1.25

1C � 1

C1�

1C2

1C

� 14

�1

12 �

412

� 13

C � 3 F

3

C � C1�C2

� 4�12

� 16 F

16

C1 C2 C12 � C1�C2

� 1�2 � 3 F

C1 � 4 F

C1 � 1 F

C1 � 3 F

C2 � 2 F

C3 � 2 F

C2 � 6 FC3 � 6 F

C1 � 4 FC2 � 12 F

C2 � 12 F

511

C1 C2 C3

1C � 1

C12�

1C3

1C �

13

�16

� 36

� 12

C � 2 F

2

C1 C2

1

C12 � 1

C1�

1C2

1

C12 �

13

�16

� 36

� 12

C12 � 2 F

C1 C2 C3 C � C12�C3

� 2�2

� 4 F

4

1.26 a A B

� C � CXY � C

A

B

B

AX

C

Y

a a

a a

a�Ca

Page 31: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

52

1C

�1

C1�

1C2

1C

�1a�

1a�

1a�C

� 2a�

1a�C

1C

�2(a�C)�a

a(a�C)

aC�a2

� aC2�3aC

2C2�aC�a

2� 0

C x ��b� b

2�4ac

2a

C ��2a� (2a)

2�4(2)(a

2)

2(2)

C �( 3�1)a

2 F

A B ( 3�1)a

2

1. 2. 3.

4. 10 5.

6 F 12 F

V � 36 V

531

1.

1) 2) -

( )

- ( )

3)

4) 3

5)

2.

3.

Page 32: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

54

4. 2

1.32

1.33

1.33

1.32

551

1.34

Page 33: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

56

1. 2.

1 3.

571

1. 6 2. 3. 4.

5.

1. 5�10 2. 2

30�35

3. 30

4.

Page 34: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

58

• 2 •

1. 2

2.

3.

• F �

kq1q2

r2

E � kQ

r2

� �

591

Process

1. 2. 3.

4.

5.

6.

7.

Attribute

1. 2. 3.

• n E � E1 � E2 � E3 �... En

• •

E �

V

d

• V �

kq

r

• 2

C � Q

V

• C � C1 � C2 � C3 �... �Cn

• 1

C�

1

C1

�1

C2

�1

C3

�... �1

Cn

Page 35: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

60

1. q1:q2

2. �2�104 8�10

�6

3. m �q g �

4. A, B C 3.0�10�6

, 1.0�10�6 -1.0�10

�6 AP � 0.6 CP � 0.3 BP � 0.1 P

5. �10 �40 3 �20

6. A B 0.3 A �1

6.1 B �0.25 6.2 B �0.25

q1 q2

m

E

611

7. 0.72 25�10�6 2 Q

6 Q 4

8. A C �12 � AB � 6 BC � 3 B A C B

9. 20 �2 20 2

10. 1 300

B A

11. 12.8 AB

2�108

11.1

11.2

u � 01 cm

Aa

B

� �e�E

E � 2�108 N/C

FE

mg

� � � � � � �

A

B

� � � � � � �

Page 36: Book IN62F2-143 ฟิสิกส์ ม5 เล่ม2

62

12. 3 2 2 �2 �4 3

13 m �q V d

g q 14. A B 25 6 P

5 Q 15 PQ

15. 14 �10�5 Q P

16. A B 6 15 A B

17. 500 25

18. 0.05 F, 400 V 15

19. 5 20 200

19.1

19.2

20. 2 12 1

A

P Q

B� �

5 cm

15 cm

25 cm

6 V