1. Electric fields are produced by electric charges and can be calculated using Coulomb's law. Positive charges produce outward electric fields while negative charges produce inward electric fields. 2. The electric field strength is directly proportional to the magnitude of the charge producing the field and inversely proportional to the distance from that charge. 3. Electric potential difference is equal to the work done moving a test charge between two points in an electric field, and is calculated by multiplying the charge by the potential.

1. SchoolDD.com
15
www.schoolDD.com

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