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ELECTROSTATICS
Outline
• Electric Force, Electric fields
• Electric Flux and Gaub law
• Electric potential
• Capacitors and dielectric (Electric storage)
The physics of charged objects
• Study of electricity aims to understand the interaction between different charged objects.
+ -
The physics of charged objects
• Study of electricity aims to understand the interaction between different charged objects.
+ +
- -
Structure of Matter
• Fundamental building blocks of the matter are atoms.
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+ + -
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Structure of Matter
• Neutral atom – electron = Positive ion
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+ + -
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C101.602charge electron -191
Structure of Matter
• Fundamental building blocks of the matter are atoms.
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++
+ + -
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-
-
-
--
Structure of Matter
• Neutral atom + electron = negative ion.
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++
+ + -
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--
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ELECTRICALLY CHARGING OBJECTS
+ - +
+- - +
+ - +
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+
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+
ELECTRICALLY CHARGING OBJECTS
+ - +
+- - +
+ - +
-
-
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+
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+
ELECTRICALLY CHARGING OBJECTS
+ - +
+- - +
+ - +
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-
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+
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+-
• In metals outer atomic electrons are not bound to any atoms (electron see).
Charging by Induction
++
+ +
+ +
+
++
+
Charging by Induction
• In metals outer atomic electrons are not bound to any atoms (electron see).
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+ +
+ +
+
++
+
-
Charging by Induction
• Same atoms have weakly bound electrons.
Electric Polarization
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+ +
-
-- -
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Electric Polarization
• Same atoms have weakly bound electrons.
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+ +
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- +
Electric Polarization
The Electric Force
Coulomb’s Law
• Quantifies the electric force between two charges.
baba QQF
Coulomb’s Law
• Quantifies the electric force between two charges.
2
1
baba r
F
Coulomb’s Law
• Quantifies the electric force between two charges.
baba
baba
ba
baba r
rQQ
krr
QQF
ˆˆ4
122
0
229
212
/10988.8
/10854.8
CNmk
and
NmC
where
0
Electric Force Field
• Gravitational force field:
Electric Force Field
+Q
Electric Force Field
+Q+q
Electric Force Field
• Definition of Electric field:
q
FE qQ
Electric Force Field
• Definition of Electric field:
qQrrkQ
EqQ
ˆ2
Electric Force Field
1r 5r
2r
+
+
+
+
+
3r
4r
Electric Force Field
• The electric field due to a number of source charges is given by the expression
N
ii
i
i
N
iii
rrq
k
rEE
12
1
ˆ
)(
Electric Force Field
Electric Force Field(Linear distribution of charge)
dL
dLdq
density charge Linear
?dEr
2rdq
kdE
Electric Force Field(Linear distribution of charge)
dL
dLdq
density charge Linear
?dE
2rdL
kdE
Electric Force Field(Linear distribution of charge)
dL
dLdq
density charge Linear
?dE
2r
dLkE
Electric Force Field(Surface distribution of charge)
dadq
ondistributi charge Surface
r?dE
da 2rdq
kdE
Electric Force Field(Surface distribution of charge)
dadq
ondistributi charge Surface
r?dE
da2rda
kdE
Electric Force Field(Surface distribution of charge)
dadq
ondistributi charge Surface
r?dE
da
surface r
dakE
2
Electric Dipole
• Electric dipole consists of a pair of point charges with equal size but opposite sign separated by a distance d.
d+ -
dqp
Electric Dipole
• Electric dipole consists of a pair of point charges with equal size but opposite sign separated by a distance d.
d+ -
Electric Dipole
• Electric dipole consists of a pair of point charges with equal size but opposite sign separated by a distance d.
d+ -
p
Electric Dipole
• Electric dipole consists of a pair of point charges with equal size but opposite sign separated by a distance d.
d+ -
dqp
Electric Dipole
• Water molecules are electric dipoles
+ +
-waterp
Exercise 1 A point charge q = -8.0 nC is located at the
origin. Find the electric field vector at the point x = 1.2 m, y = -1.6 m
m 2.1
-
m 6.1mr 0.2
m 2.1
-
m 6.1mr 0.2
jEiEE yxˆˆ
m 2.1
-
m 6.1mr 0.2
)ˆsinˆ(cos jiEE
m 2.1
-
m 6.1mr 0.2
jCN iCN E ˆ/14ˆ/11
Exercise 2
An electric dipole consists of a positive charge q and negative charge –q separated by a distance 2a, as shown in the figure below. Find the electric field due to these charges along the axis at the point P, which is the distance y from the origin. Assume that y>>a.
q q
r
aa
r
Vector Flux
Vector Flux
Vector Flux
• Definition of flux:
Av
Electric Flux
Electric Flux
AdEE
Gaub’s Law
Surface Enclosed
EnclosedQAdE
0
Gaub’s Law
dA EAdEd E
+r
Gaub’s Law
dA EE
+r
Gaub’s Law
dArkQ
E 2
+r
Gaub’s Law
0
22
0
44
Q
rr
QE
+r
Exercise 3dE
Solution
Coulomb’s Law
22 RdAk
Rkdq
dE
Solution
Infinitesimal area of disk
rdrdA 2
Solution
Infinitesimal area of disk
2
2
Rrdrk
dE
Solution
Y-component of E-field element
cos2
cos2Rrdrk
dEdEy
Solution
RL
cos
Solution
Y-component of E-field element
RL
Rrdrk
dEy 2
2
Solution
Y-component of E-field element
04
1
k
Solution
Y-component of E-field element
2/3220 )(2 Lr
rdrLdEy
Solution
Y-component of E-field element
0
02/322
02/322
0
2
1
)(
)(2
y
y
E
LLrrdr
Lrrdr
LE
identity the Using
Two Oppositely charged Parallel Plates (Capacitor)
Two Oppositely charged Parallel Plates (Capacitor)
?E
Exercise 4
00
LQAdE
Gauss
0
0
2
2
rE
LrLE
Area rL2cylinder a of
Electric Potential
+Q+q
Electric Potential
+Q
Electric Potential
test
test
QQ on
oodneighboreh its in source due Ppoint aat potential
)( PWork
Electric
Electric Potential
PSource
P
P
test
rdrr
kQ
rdE
rdFQ
Electric
ˆ
1
2
oodneighboreh its in source due Ppoint aat potential
Electric Potential
rQ
rkQ SourceSource
04V(r)
1J/C V 1:Unit
Electric Potential
N
i i
i
rQ
104
1PV
Electric potential at position P due to a system of N source charges is given by:
Electric Potential
• Potential difference:
Electric Potential
• Potential difference:
Electric Potential
b
a
r
r
absourceab
rdE
rrkQrVrVV
11)()(
Two Oppositely charged Parallel Plates (Capacitor)
constantE
V
Two Oppositely charged Parallel Plates (Capacitor)
Ed
rrE
drE
rdEV
ba
r
r
r
r
b
a
b
a
)(
Capacitors and di-electrics
• Capacitors store electric potential energy
Battery
VV
VQ
C
plates across Voltage
plate each on stored ChargeeCapacitanc
)(1/11 FfaradVCC
Capacitors and di-electrics
E
E
AQ
EEE
0
0
resultant
Capacitors and di-electrics
Capacitors and di-electrics
• We can therefore express the voltage across the capacitor plates as follows:
dA
QEdV
0
• Hence
dA
AQd
QVQ
C 0
0
Exercise 3
A parallel-plate capacitor has an area of A = 2 cm2 and a plate separation of d =1mm.
(a) Find its capacitance. (answer = 1.77pF)
(b) If the plate separation of this capacitor is increased to 3 mm, find the capacitance. (answer = 0.59 pF).
Capacitors and di-electrics
• Capacitors in Parallel
Capacitors and di-electrics
• Di-electric material inside a parallel Electric field.
Capacitors and di-electrics
• Di-electric material between parallel capacitor plates.
Capacitors and di-electrics
• Di-electric material between parallel capacitor plates.
vacuumelectricdi KCC
Capacitors and di-electrics
• Di-electric material between parallel capacitor plates.
vacuumvacuumelectricdielectricdi VCVCQ
constant remains Charge
Capacitors and di-electrics
• Di-electric material between parallel capacitor plates.
vacuumKVelectric-diV
Capacitors and di-electrics
• Di-electric material between parallel capacitor plates.
vacuumKE
Ed
electric-diE
V Since