2. F ˆ F www.schoolDD.com 1
15
15.1 ˂
˂ F F
F F F ˂ F F
F F F F F
F
ˈ ˂ F
1. ˂ 2
- ˂ ( + )
- ˂ ( - )
2. F ˂ F ˈ 2
- ˈ F F
- ˈ F
F F F
.
.
.
F
3. F ˆ F www.schoolDD.com 2
F F F
F F
F F F ˈ ˂ F
F F
F F
F ˈ
ˈ
F ( F F F ˈ
F F ˈ )
• F
• F
• F F
•
• F
• F
• F ˂
•
•
•-
F +
ˈ
ˈ ˈ ˂
ˈ
F F
F F
F
4. F ˆ F www.schoolDD.com 3
15.2 F ˂
F F F
F ˂ F F ˈ F F F ˈ F
F
- ˈ ˂ F
- ( > )
- ( > )
- F
- F F F ˂ F F ˈ ˂
15.3 ˂ ˂
˂ (Conductor) F ˂ F F F
F
˂ (Insulator) F ˂ F F F F
- F F F
F F F F F F F
F F
F F F F
ˈ F
ˈ
˂F F F
( )
F
5. F ˆ F www.schoolDD.com 4
15.4 ˂
˂ ˈ F ˈ ˂ ˂
F F ˈ 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
6. F ˆ F www.schoolDD.com 5
F ˂
˂ F
15.5 F F
F F F F F ˈ F
F
F = F ( , N) ( )
K = F = 9x109
(N m2
/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
F
ˈ
˂
F F
˂
F
F ן Q1Q2
F ן
ଵ
୰మ
r
FF
F
F
F
F
Q2Q1
F =
۹ۿۿ
ܚ
F
7. F ˆ F www.schoolDD.com 6
F F =
୕భ୕మ
୰మ
=
ଽ୶ଵవ୶ଵ୶ଵషల୶ଵ୶ଵషల
ଶ.మ
F = 2.25x10-3
N Ans ( ˈ + )
F 2
F A B C q1 = 3 ߤC , q2 = 3 ߤC q3 = -4 ߤC F AB =
3 m. BC. = 3 m. F F B
F F =
୕భ୕మ
୰మ
F1 =
ଽ୶ଵవ୶ଷ୶ଵషల୶ଵ୶ଵషల
ଷ.మ
= 3x10-3
N
F2 =
ଽ୶ଵవ୶ଵ୶ଵషల୶ସ୶ଵషల
ଷ.మ
= 4x10-3
N
F F B F
R = ඥFଵ
ଶ
Fଶ
ଶ
= ඥሺ3x10ିଷሻଶ ሺ4x10ିଷሻଶ
R = √25x10ି
R = 5.0x10-3
N Ans
R AB F
tan θ =
మ
భ
=
ସ୶ଵషయ
ଷ୶ଵషయ
=
ସ
ଷ
θ = 53° Ans
Q2 = +1 ߤCQ1 = +1 ߤC
r = 2.0 m
F B
θ
R
F1
F2
B
B
C
A
3.0 m
q2 = 1 ߤCq1 = 3 ߤC
3.0 m
Q3 = -4 ߤC
8. F ˆ F www.schoolDD.com 7
15.6 ˂
˂ (Electric Field) E F F F F
˂ ˂ ˈ F F + q
F ˈ F F ( N/C)
F =
୕భ୕మ
୰మ
F F =
୕୯
୰మ
E =
୯
F E =
୕୯
୰మ
/q
E =
۴
ܙ
E =
۹ۿ
ܚ
ˈ F ˂
Q F F ˈ r
E ן Q E ן
ଵ
୰మ
r
Fሬറ Eሬሬറ
+q+Q
Fሬറ Eሬሬറ
+q-Q
+Q -Q
˂ +Q ˂ -Q
E = ୕
୰మ
r
Q
9. F ˆ F www.schoolDD.com 8
F 3
˂ Q 1 ߤC F 1 m. F
ˈ
˂ E =୕
୰మ
=ଽ୶ଵవ୶ଵ୶ଵషల
ଵ.మ
E = 9.0x103
N/C
˂ Q F F 9.0x103
N/C Ans
˂ ˂ F +q
F +q F F ˈ r ˈ ˂
Q ˈ ˂ F
Q ˈ ˂ F F
F 4
F X Z Q1 Q2 -4 ߤC F 2 ߤC F
XY F 2.0 YZ F 3.0 ˂ Y
θ
E
E2
E1
Y
3.0 m
Z
YX
Q2 = 2x10-6
C
2.0 m
Q1 = -4x10-6
C
˂ F Y
E
E
r = 1.0 m
+Q
r = 1.0 m
-Q
10. F ˆ F www.schoolDD.com 9
˂ ˈ F ˂ F Y ˈ ˂ F ˂
Q1 Q2
˂ Q1 E1 =୕భ
୰భ
మ
=ଽ୶ଵవ୶ସ୶ଵషల
ଶ.మ
E1 = 9.0x103
N/C ( YX)
˂ Q2 E2 =୕మ
୰మ
మ
=ଽ୶ଵవ୶ଶ୶ଵషల
ଷ.మ
E2 = 2.0x103
N/C ( ZY)
˂ F F Y F
E = ඥEଵ
ଶ
Eଶ
ଶ
= ඥሺ9x10ଷሻଶ ሺ2x10ଷሻଶ
E = √85x10
E = 9.2x103
N/C Ans
˂ F YX F
tan θ =
మ
భ
=
ଶ୶ଵయ
ଽ୶ଵయ
= 0.22
θ = 12.5° Ans
F ˂
1. + q F ˂ Q
2. q F ˂ Q
Fሬറ
FሬറEሬሬറ+q+Q
Eሬሬറ +q-Q F = qE
Fሬറ
Fሬറ Eሬሬറ
-q+Q
Eሬሬറ -q-Q
F = qE
11. F ˆ F www.schoolDD.com 10
- ˂ ˂ F + q F
- F F F F ( F , )
15.7 F ˂
F ˂ F F F ˂
F 1 F ˂ ˈ F ˂ F ˈ
F F +q
F ˂
1. F
F ˂ + F ˂ -
E
E2
E1
-Q2
+Q1
F ˂ +Q1 Q2
-+
E
-
+
E
˂ F
F
F ˂
ˈ F
12. F ˆ F www.schoolDD.com 11
2. F F
3.
- F ˂ F F F
- F ˂ F ˂ F
- F ˂ F F ˂ F
- ˂ F
F 5
8.4x10-14
F ˂ F
F ˂ ˈ 4x106
F F ( F F
)
F F a = 0
F FE = mg
qE = mg (E =
୯
)
q(4x106
) = 8.4x10-14
x10
q = 2.1x10-19
-2.1x10-19
C Ans ( FE F +)
-
+
E
FE
mg
-
+
E = 4x106
F
F ˂ F
F F ˂
F ˂ F F
F F ˂ ˂
F ˈ F
13. F ˆ F www.schoolDD.com 12
F 6
F A B F A B F ˂
15.8 F ˂ F F ˂
F ˂
F F F F m F B F F F F A ˈ h
F F ˂
BA
E A
B
E
V =
۳ܘ
ܙ
F F F Ep
F B F F A F F mgh F
A B F
EPB - EPA = mgh
EPB - EPA = W՜
EPA
EPB
A
B
g
F F
mg
mg
m
m
h
F A B ˂ E
+q F B B A F
F B F ˂ F F A ( F
F F F F )
EPB > EPA
EP
q
q ˂ E
F ˂ Ep ˂ F F
F ˂ V F ˂ F 1 F
F ˂ ˈ F F ˈ F F
F (V)
EPB EPA
+q
AB
E
14. F ˆ F www.schoolDD.com 13
F F ˂ F F ˂ F F B A ( VB VA ) F F
1 F F A B
F A F F(∞) VA = 0 F VB = ಮ՜ా
୯
F F F F ˂ F 1 F F F
15.8.1 F ˂
F ˂ F F F Q ˈ r F
- F ˂ ˈ F F ˂ F F ˂ ˈ F F ˂ ˈ
F ˂ ( + > 0 > - )
- F ˂ = F ˂ F ( + , - )
- F ˂ ˈ F F ( r = ∞ ---> V =
୕
ஶ
= 0 )
F 7
F ˂ Q F 1 F
. 2.0x10-6
F . -2.0x10-6
F
. Q = 2x10-6
C
V = ୕
୰
= ଽ୶ଵవ୶ଶ୶ଵషల
ଵ.
V = 1.8x104
V Ans
V =
۹ۿ
ܚ
Q V
r
Q V = ?
r = 1.0 m
V = F ˂ F ˈ F
Q
V = ౦
୯
VB VA = ౦ా
୯
- ౦ఽ
୯
= ౦ా ି ౦ఽ
୯
VB VA =
܅ۯ՜۰
ܙ
VAVB
q
AB
E
15. F ˆ F www.schoolDD.com 14
. Q = -2x10-6
C
V = ୕
୰
= ଽ୶ଵవ୶ିଶ୶ଵషల
ଵ.
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
. VD = ?
VD ˈ ˂ F A, B C
V = ୕
୰
F ˂ D A = ଽ୶ଵవ୶ଵ୶ଵషల
.ଶ
= 4.5x104
V
F ˂ D B = ଽ୶ଵవ୶ିଶ୶ଵషల
.ସ
= -4.5x104
V
F ˂ D C = ଽ୶ଵవ୶ଷ୶ଵషల
.ଷ
= 9.0x104
V
VD = (4.5x104
) + (-4.5x104
) + (9.0x104
)
VD = 9.0x104
V Ans
.
F F ˂ VB VA =
ఽ՜ా
୯
F A F F VA = 0 B F F D F
VD =
ಮ՜ీ
୯
Wஶ՜ୈ = qVD
= 1.2x10-6
x9x104
W∞՜D = 0.108 J Ans
0.4 m
0.3 mD
C
B
A
0.2 m
1x10-6
C
-2x10-6
C
3x10-6
C
16. F ˆ F www.schoolDD.com 15
15.8.2 F ˂
- F ˂ F F F ୕
ୟ
a
- F ˂ F F F ୕
୰
r F F
F
F 9
10 2 F P Q R F F F
ˈ 5,10 20
. F ˂ P Q R
. F 1x10-9
F F P Q R
. F -1x10-9
F R Q
. VP , VQ VR = ?
V = ୕
୰
VP = VQ = ଽ୶ଵవ୶ିଶ୶ଵషల
.ଵ
= -1.8x104
V Ans
VR = ଽ୶ଵవ୶ିଶ୶ଵషల
.ଶ
= -0.9x104
V Ans
. W = ?
F F ˂ VB VA =
ఽ՜ా
୯
F A F F VA = 0 F
Q
20 cm
10 cm
Q = -2x10-6
C
P R
5 cm
V = ۹ۿ
ܚ
V = ۹ۿ
܉ a
r
17. F ˆ F www.schoolDD.com 16
VB =
ಮ՜ా
୯
Wஶ՜ = qVB (B = P)
Wஶ՜ = qVP
= 1.0x10-9
x-1.8x105
W∞՜P = Wஶ՜୕ = -1.8x10-4
J Ans ( ˈ F )
Wஶ՜ୖ = qVR
= 1.0x10-9
x-0.9x105
W∞՜R = -0.9x10-4
J Ans
. Wୖ՜୕ = ? q = -1x10-9
C
F F ˂ VB VA =
ఽ՜ా
୯
Wୖ՜୕ = q (VQ VR) (A = R, B = Q)
= -1.0x10-9
(-1.8x105
(-0.9x105
))
Wୖ՜୕ = 0.9x10-4
J Ans ( ˈ F )
15.8.3 F F F F ˂
F F ˂ VB VA =
ఽ՜ా
୯
+q F A ˂ F qE
˂ ( F ) F F +q A B F (a=0) F
F F qE F ˂
+q A B F
W՜ = F d
= qE d
F F F F
VB VA =
qE d
୯
+
+
+
+
F +q qE
d
AB
E
-
-
-
-
18. F ˆ F www.schoolDD.com 17
E ˈ ˂ F ˈ F F (V/m)
d ˈ F A B F ˈ (m)
F 10
F F F F 20 F F F F ˈ 400 F
. ˂ F F F
. F 9x10-31
-1.6x10-19
F F
F F F
. 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
VB - VA = Ed
E =
୯
(
େ
x ୫
୫
=
େ ୫
=
୫
)
-
-
-
-
+
+
+
+
B A
d = 20 cm
VB VA = 400 V
19. F ˆ F www.schoolDD.com 18
F 11
F F F 2 F ˂ F F F
9x10-31
1.6x10-19
F F F F F F
F F F ˈ F
∑ F୷ = ma (a=0)
F = mg
qE = mg
E =
୫
୯
=
ଽ୶ଵషయభ୶ଵ
ଵ.୶ଵషభవ
VB - VA = Ed
=
ଽ୶ଵషయభ୶ଵ
ଵ.୶ଵషభవ
(0.02)
VB - VA = 1.12x10-12
V Ans
F ˂
1. F F F A B 1 F A B
VB VA =
ఽ՜ా
୯
2. F ˂ B 1 F ∞ B
VB = ಮ՜ా
୯
3. F ˂ Q r
mg
d = 2 cm
F = qE
+ + + +
- - - -
A
B
F F F ˈ
+ F F ˈ - F
F F
VAVB
q
AB
E
Vஶ = 0VB
q
∞B
E
Q V =
୕
୰
r
20. F ˆ F www.schoolDD.com 19
4. F ˂ Q
4. F ˂ F + , - 0 F
15.9
(Capacitor) ˈ ˂ F F F
(Capacitance) C F F F (Q)
F F ˂ (V) F ˈ F F F (C /V) (F)
r = a F ˂ V =
୕
ୟ
C =
୕
=
୕
ే్
=
ୟ
C ן a
- F >
F ˂ F (+) F F ˂ (+) F F (-) F F ˂ (-)
C =
ۿ
܄
V = ۹ۿ
ܚ
V = ۹ۿ
܉ a
r
F F
F
F (+ -) F F Q = CV
C+Q -Q
V
F
F
21. F ˆ F www.schoolDD.com 20
F 12
20 F ˂ F
F 13
˂ F ˂ 10 F ˂ 0.2
F 14
70 F F F 20 F
15.9.1
U F F F F F (V) ˂
(Q) F ˈ (J)
a = 20 cm C =
୕
=
୕
ే్
=
ୟ
=
.ଶ
ଽ୶ଵవ
C = 2.2x10-11
F Ans
V = 10 V
C = 0.2 ߤ F
C =
୕
Q = CV
= 0.2x10-6
x10
Q = 2.0x10-6
C Ans
C = 70 ߤF
+Q -Q
V = 20 V
C =
୕
Q = CV
= 70x10-6
x20
Q = 1.4x10-3
= 1400 ߤC Ans
v
Q
F F
˂
U =
QV
22. F ˆ F www.schoolDD.com 21
Q V F F C =
୕
Q = CV
F Q ן V plot Q V F F
F 15
50 F F F F 10 F
U =
ଵ
ଶ
QV ---1
F V Q C =
୕
Q = CV = 50x10-6
x10 = 500x10-6
C
F Q V 1 , U =
ଵ
ଶ
500x10-6
x10
U = 2.5x10-3
J Ans
15.9.2 F
F F ˂ 2
1. F
ˈ F F F F
F F F F ˂ F
F F
1. F F F Q = Q1 = Q2 = Q3
2. F F F F F V = V1 + V2 + V3
V = V1 + V2 + V3
C =
୕
V =
୕
େ
୕
େ
=
୕భ
େభ
+
୕మ
େమ
+
୕య
େయ
C+Q -Q
V
V
V2 V3V1
Q
Q
C1
Q1
C3
Q3
C2
Q2
23. F ˆ F www.schoolDD.com 22
2. F
ˈ F F F
F F F
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
F 16
10 20 F
F
۱
=
۱
+
۱
+
۱
C = C1 + C2 + C3
C2= 20 ߤFC1= 10 ߤF
Q
QQ1
V
Q2
V1 = V2 = V3
C3
Q
Q
Q1
V
Q3
C2
Q2
C1
24. F ˆ F www.schoolDD.com 23
ଵ
େ
=
ଵ
େభ
+
ଵ
େమ
=
ଵ
ଵఓ
+
ଵ
ଶఓ
=
ଶାଵ
ଶఓ
=
ଵ
.ఓ
C = 6.7 ߤF Ans
F
C = C1 + C2
= 10ߤF + 20ߤF
C = 30 ߤF Ans
F 17
2 4 F F F F 120
F F
. .
. F
Q C =
୕
Q = C V ---1
F V = 120 V C
ଵ
େ
=
ଵ
େభ
+
ଵ
େమ
C2= 20 ߤF
Q
Q
Q2
Q1
V
C1= 10 ߤF
C2= 4 ߤFC1= 2 ߤF
Q
QQ1
V = 120 V
Q2
25. F ˆ F www.schoolDD.com 24
=
ଵ
ଶఓ
+
ଵ
ସఓ
=
ଶାଵ
ସఓ
=
ଵ
ଵ.ଷଷఓ
C = 1.33 ߤF
F 1 , Q = 1.33x10-6
x120
Q = 160x10-6
C Ans
U U =
ଵ
ଶ
QV
U =
ଵ
ଶ
Q V
=
ଵ
ଶ
(160x10-6
)(120)
U = 0.0096 J Ans
. F
C C = C1 + C2
= 2ߤF + 4ߤF
C = 6 ߤF
Q C =
୕
Q = C V
Q = 6.0x10-6
x120
Q = 720x10-6
C Ans
U U =
ଵ
ଶ
QV
U =
ଵ
ଶ
Q V
=
ଵ
ଶ
(720x10-6
)(120)
U = 0.043 J Ans
C1= 4 ߤF
Q
Q
Q2
Q1
V
C1= 2 ߤF
26. F ˆ F www.schoolDD.com 25
F 18
140 F F 1 F F
F F 1,000 F
F n
F C = C1 + C2 + C3 + Cn
F C1 = C2 = C3 = Cn = 140 ߤF
C = 140 (n) ߤF
C =
୕
C =
୕
140 (n) x10-6
=
ଵ.
ଵ
n =
ଵ
ଵସ
= 7.1
n = 8 Ans
F 19
C1 6 C2 12 C3 8
F F F 100 F F F F
Cn
Q
Q = 1 C
Q1
V = 1000 V
Qn
C2
Q2
C1
C2
C1
100 V C3
27. F ˆ F www.schoolDD.com 26
C1 C2 F F F C3 C1 C2
ଵ
େ
=
ଵ
େభ
+
ଵ
େమ
ଵ
େభమ
=
ଵ
ఓ
+
ଵ
ଵଶఓ
=
ଶାଵ
ଵଶఓ
=
ଵ
ସఓ
C12 = 4 ߤF
Q12 C =
୕
Q12 = C12V
= 4x10-6
x100
Q12 = 400 ߤC
C1 C2 F Q1 = Q2 = Q12 = 400 ߤC Ans
Q3 C =
୕
Q3 = C3V
= 8x10-6
x100
Q12 = 800 ߤC Ans
F F F C =
୕
V =
୕
େ
V1 =
୕భ
େభ
=
ସఓେ
ఓ
= 66.67 V Ans
V2 =
୕మ
େమ
=
ସఓେ
ଵଶఓ
= 33.33 V Ans
(Check V1 + V2 = V , 66.67 + 33.33 = 100 V --> OK! )
V3 =
୕య
େయ
=
଼ఓେ
଼ఓ
= 100 V Ans
(Check V3 = V , 100 V = 100 V --> OK! )
F U =
ଵ
ଶ
QV
U1 =
ଵ
ଶ
Q1 V1
=
ଵ
ଶ
(400x10-6
)(66.67)
U1 = 0.013 J Ans
U2 =
ଵ
ଶ
Q2 V2
=
ଵ
ଶ
(400x10-6
)(33.33)
U2 = 0.0067 J Ans
28. F ˆ F www.schoolDD.com 27
U3 =
ଵ
ଶ
Q3 V3
=
ଵ
ଶ
(800x10-6
)(100)
U3 = 0.04 J Ans
