1. SchoolDD.com
15
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2. 15
15.1
F F
F F F F F
F F F F F
F
F
1. 2
- (+)
- (-)
2. F F 2
- F F
- F
.
.
.
F
F F F
F F www.schoolDD.com 1

3. F F F
F F
F F F F
F F
F F
F
F ( F F F
F F )
F + • F
• F
• F F
•
• F
• F
• F
•
•
- •
F
F F
F F
F F www.schoolDD.com 2

4. F F
F F F F
F
15.2 F
F FF
F F F F F F F
F
- F
- ( > )
- ( > )
- F
- F F F F F
15.3
(Conductor) F F F F
F
(Insulator) F F F F F
- F F F
FF F F F F F
( )
F F F F
F F www.schoolDD.com 3

5. F ( ) F F F F F
F F F F
15.4
F
F F F F F F
F F F F F F
( F ) F F
F (- -) (- +) F
> F F F
F F F
F F www.schoolDD.com 4

6. F
F
F F F F
F
F
15.5 F F
F F FF F F
F
Q1 Q2
F F F Q1Q2
r F
F F
F F F
F=
F= F ( , N) ( )
9 2
K= F = 9x10 (N m /C)
Q1 = 1( F , C)
Q2 = 2( F , C)
r= F F ( , m)
F 1
Q1 Q2 F +1 F F 2.0 F
F
F F www.schoolDD.com 5

7. Q1 = +1 C Q2 = +1 C
r = 2.0 m
F F=
=
F = 2.25x10-3 N Ans ( + )
F 2
F AB C q1 = 3 C , q 2 = 3 C q3 = -4 C F AB =
3 m. BC. = 3 m. F F B
Q3 = -4 C
C
F2 R
3.0 m
q1 = 3 C q2 = 1 C
A B
3.0 m B F1
F B
F F=
F1 = = 3x10-3 N
F2 = = 4x10-3 N
F F B F
R= =
R=
R = 5.0x10-3 N Ans
R AB F
tan = = =
= 53° Ans
F F www.schoolDD.com 6

8. 15.6
(Electric Field) E F F F F
F F +q
F F F ( N/C)
+Q +q
-Q
E=
+q
r
F=
FF=
E=
FE= /q
Q E= F
E= Q F F r
r E Q E
+Q -Q
+Q -Q
F F www.schoolDD.com 7

9. F 3
Q 1 C F 1 m. F
E
E
+Q -Q
r = 1.0 m r = 1.0 m
E=
=
E = 9.0x103 N/C
Q F F 9.0x103 N/C Ans
F +q
F +q F F r
Q F
Q F F
F
4
F X Z Q1 Q2 -4 C F 2 C F
XY F 2.0 YZ F 3.0 Y
Q2 = 2x10-6 C
Z
E1
Y
3.0 m
E
Q1 = -4x10-6 C E2
X Y
2.0 m
F Y
F F www.schoolDD.com 8

10. F F Y F
Q1 Q2
Q1 E1 =
=
E1 = 9.0x103 N/C ( YX)
Q2 E2 =
=
E2 = 2.0x103 N/C ( ZY)
F F Y F
E= =
E=
E = 9.2x103 N/C Ans
F YX F
tan = = = 0.22
= 12.5° Ans
F
1. +q F Q
+Q +q
-Q F = qE
+q
2. q F Q
+Q -q
F = qE
-Q -q
F F www.schoolDD.com 9

11. - F +q F
- F F F F( F , )
15.7 F
F F F F
F + F -
F 1 F F F
F F +q
E1
E
E2
+Q1 -Q2
F +Q1 Q2
F
1. F
E + F
F
E
F
- F
+ -
F F www.schoolDD.com 10

12. 2. F F
F F
F F
3.
F F F
F F
F F
- F F F F
- F F F
- F F F F
- F
F 5
8.4x10-14 F F
F 4x106 F F ( F F
)
+ +
FE F
E E = 4x106
mg
- -
F F a=0
F
FE = mg
qE = mg (E = )
q(4x106) = 8.4x10-14x10
q = 2.1x10-19
-2.1x10-19 C Ans ( FE F +)
F F www.schoolDD.com 11

13. F 6
F A B F A B F
E A
A B E
B
15.8 F F F
F
F F F F m F B F F F F A h
B EPB
m F F F Ep
g mg h
F B F F A F F mgh F
F F A B F
m A EPA EPB - EPA = mgh
EPB - EPA =
mg
q E
F Ep F F
q
EP
F V F F 1 F
F F F F F
F (V)
V=
F F
F A B E
E
+q F B B A F
B A
+q F B F F F A( F
F F F F )
EPB EPA EPB > EPA
F F www.schoolDD.com 12

14. F F F F F F B A ( VB VA ) F F
1 F F A B
E
B A V=
q VB VA = VB VA = -
VB VA =
F A F F( ) VA = 0 F VB =
F FF F F 1 F F F
15.8.1 F
F F F F Q r F
Q V
V= F F F
r
V= Q
- F F F F F F F
F (+>0>-)
- F = F F ( +,-)
- F F F ( r = ---> V = =0)
F 7
F Q F 1 F
-6
. 2.0x10 F . -2.0x10-6 F
Q V=?
r = 1.0 m
. Q = 2x10-6 C
V=
=
V = 1.8x104 V Ans
F F www.schoolDD.com 13

15. . Q = -2x10-6 C
V=
=
V = -1.8x104 V Ans
F 8
F A, B C 1x10-6 , -2x10-6 3x10-6 F
. F D
. F 1.2x10-6 F F D
-2x10-6 C
B
0.4 m 3x10-6 C
1x10-6 C C
A
D 0.3 m
0.2 m
. VD = ?
VD F A, B C
V=
F D A= = 4.5x104 V
F D B= = -4.5x104 V
F D C= = 9.0x104 V
VD = (4.5x104) + (-4.5x104) + (9.0x104)
VD = 9.0x104 V Ans
.
F F VB VA =
F A F F VA = 0 B F F D F
VD =
= qVD
= 1.2x10-6 x9x104
= 0.108 J Ans
F F www.schoolDD.com 14

16. 15.8.2 F
V= a V=
r
- F F F F a
- F F F F r F F
F
F 9
10 2 F PQ R F F F
5,10 20
. F PQ R
. F 1x10-9 F F PQ R
. F -1x10-9 F R Q
Q = -2x10-6 C
P Q R
5 cm
10 cm
20 cm
. VP , VQ VR = ?
V=
VP = VQ = = -1.8x104 V Ans
VR = = -0.9x104 V Ans
. W=?
F F VB VA =
F A F F VA = 0 F
F F www.schoolDD.com 15

17. VB =
= qVB (B = P)
= qVP
= 1.0x10-9x-1.8x105
= = -1.8x10-4 J Ans ( F )
= qVR
= 1.0x10-9x-0.9x105
= -0.9x10-4 J Ans
. =? q = -1x10-9 C
F F VB VA =
= q (VQ VR) (A = R, B = Q)
= -1.0x10-9(-1.8x105 (-0.9x105))
= 0.9x10-4 J Ans ( F )
15.8.3 F F F F
E
+ -
F +q qE
+ -
B A
+ d
-
+ -
F F VB VA =
+q F A F qE
( F ) F F +q A B F (a=0) F
F F qE F
+q A B F
= Fd
= qE d
F F F F
VB VA =
F F www.schoolDD.com 16

18. VB - VA = Ed
E= ( x = = )
E F F F (V/m)
d F A B F (m)
F 10
F F F F 20 F F F F 400 F
. F F F
. F 9x10-31 -1.6x10-19 F F
F F F
VB VA = 400 V
B A
+ -
+ -
+ -
+ -
d = 20 cm
.E=?
E VB - VA = Ed
400 = E (0.20)
E = 2x103 V/m Ans
. 9x10-31 kg 1.6x10-19 C , a = ?
F F a A --> B F
F = ma
qE = ma
1.6x10-19(2x103) = 9x10-31(a)
a = 3.5x1014 m/s2 Ans
F F www.schoolDD.com 17

19. F 11
F F F 2 F F F F
-31 -19
9x10 1.6x10 F F F F F F
F F F F
+ + + + B
F = qE
F F F
d = 2 cm + F F - F
mg F F
A
- - - -
= ma (a=0)
F = mg
qE = mg
E= =
VB - VA = Ed
= (0.02)
VB - VA = 1.12x10-12 V Ans
F
1. F F F A B 1 F A B
E
B A
q VB VA =
VB VA
2. F B 1 F B
E
B
q VB =
VB =0
3. F Q r
Q V=
r
F F www.schoolDD.com 18

20. 4. F Q
V= a V=
r
4. F F +,- 0 F
15.9
(Capacitor) F F F
(Capacitance) C F F F (Q)
F F (V) F F F F (C /V) (F)
C=
r=a F V=
C=
=
=
C a
- F >
F F (+) F F (+) F F (-) F F (-)
+Q
F F
C -Q
F
V F (+ -) F F Q = CV
F
F
F F www.schoolDD.com 19

21. F 12
20 F F
a = 20 cm C= =
=
=
C = 2.2x10-11 F Ans
F 13
F 10 F 0.2
V = 10 V
C=
C = 0.2 F
Q = CV
= 0.2x10-6 x10
Q = 2.0x10-6 C Ans
F 14
70 F F F 20 F
C = 70 F
+Q -Q
C=
V = 20 V
Q = CV
= 70x10-6 x20
Q = 1.4x10-3 = 1400 C Ans
15.9.1
U F F F F F (V)
(Q) F (J)
Q
U = QV
F F
v
F F www.schoolDD.com 20

22. +Q C -Q
Q V F F C=
Q = CV V
FQ V plot Q V F F
F 15
50 F F F F 10 F
U = QV ---1
FV Q C=
Q = CV = 50x10-6 x10 = 500x10-6 C
F Q V 1 , U = 500x10-6x10
U = 2.5x10-3 J Ans
15.9.2 F
F F 2
1. F
F F F F
C1 C2 C3
Q1 Q2 Q3 Q
V1 V2 V3
V
Q
F F F F F
FF
1. F F F Q = Q1 = Q2 = Q3
2. F F F F F V = V1 + V2 + V3
V = V1 + V2 + V3
C= V=
= + +
F F www.schoolDD.com 21

23. = + +
2. F
F F F
V1 = V2 = V3
C1
Q1 C2
Q2
Q3 C3
Q
V
Q
F FF
1. F F F Q = Q1 + Q2 + Q3
2. F F F F F F F V = V1 = V2 = V3
Q = Q1 + Q2 + Q3
C= Q = CV
C V = C1 V1 + C2 V2 + C3 V3
C = C1 + C2 + C3
F 16
10 20 F
C1= 10 F C2= 20 F
F
Q1 Q2 Q
V
Q
F F www.schoolDD.com 22

24. = +
= +
= =
C = 6.7 F Ans
F
C1= 10 F
Q1
C2= 20 F
Q2
Q
V
Q
C = C1 + C2
= 10 F + 20 F
C = 30 F Ans
F 17
2 4 F F F F 120
F F
. .
. F
C1= 2 F C2= 4 F
Q1 Q2 Q
V = 120 V
Q
Q C=
Q =C V ---1
F V = 120 V C
= +
F F www.schoolDD.com 23

25. = +
= =
C = 1.33 F
F 1, Q = 1.33x10-6 x120
Q = 160x10-6 C Ans
U U = QV
U = Q V
= (160x10-6)(120)
U = 0.0096 J Ans
. F
C1= 2 F
Q1
C1= 4 F
Q2
Q
V
Q
C C = C1 + C2
= 2 F+4 F
C =6 F
Q C=
Q =C V
Q = 6.0x10-6 x120
Q = 720x10-6 C Ans
U U= QV
U = Q V
= (720x10-6)(120)
U = 0.043 J Ans
F F www.schoolDD.com 24

26. F 18
140 F F1 F F
F F 1,000 F
C1
Q1 C2
Q2
Qn Cn
Q =1C
V = 1000 V
Q
F n
F C = C1 + C2 + C3 + Cn
F C1 = C2 = C3 = C n = 140 F
C = 140 (n) F
C=
C =
140 (n) x10-6 =
n= = 7.1
n=8 Ans
F 19
C1 6 C2 12 C3 8
F F F 100 F F F F
C1
100 V C3
C2
F F www.schoolDD.com 25

27. C1 C2 F F F C3 C1 C2
= +
= +
= =
C12 = 4 F
Q12 C=
Q12 = C12V
= 4x10-6 x100
Q12 = 400 C
C1 C2 F Q1 = Q2 = Q12 = 400 C Ans
Q3 C=
Q3 = C3V
= 8x10-6 x100
Q12 = 800 C Ans
F F F C= V=
V1 = = = 66.67 V Ans
V2 = = = 33.33 V Ans
(Check V1 + V2 = V , 66.67 + 33.33 = 100 V --> OK! )
V3 = = = 100 V Ans
(Check V3 = V , 100 V = 100 V --> OK! )
F U= QV
U1 = Q1 V1
= (400x10-6)(66.67)
U1 = 0.013 J Ans
U2 = Q2 V2
= (400x10-6)(33.33)
U2 = 0.0067 J Ans
F F www.schoolDD.com 26

28. U3 = Q3 V3
= (800x10-6)(100)
U3 = 0.04 J Ans
F F www.schoolDD.com 27