1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:
-
Upload
francis-day -
Category
Documents
-
view
214 -
download
2
Transcript of 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:
![Page 1: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/1.jpg)
1
24 Electrostatic Potential Energy
![Page 2: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/2.jpg)
2
![Page 3: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/3.jpg)
3
ji ij
ji
r
qkq
2
1
DA
AD
AD
DA
CA
AC
AC
CA
BA
AB
AB
BA
r
qkq
r
qkq
r
qkq
r
qkq
r
qkq
r
qkq
2
1
DC
CD
CD
DC
DB
BD
BD
DB
CB
BC
BC
CB
r
qkq
r
qkq
r
qkq
r
qkq
r
qkq
r
qkq
2
1
![Page 4: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/4.jpg)
4
ji ij
ji
r
qkq
2
1
a
kq
a
kq
224
22
aarij 2,
Example as shown:
242
24
22
a
kq
a
kq
![Page 5: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/5.jpg)
5
SI Unit: farad [F] = C/V
Capacitance: Charge Storage per Volt Applied
![Page 6: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/6.jpg)
6
Real Parallel-Plate Capacitor
Note:
• Uniform Field
• Fringing
![Page 7: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/7.jpg)
7
Parallel Plate Capacitor
o
E
E is nearly uniform
o
dEdV
V
QC
A
od / d
Ao
![Page 8: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/8.jpg)
8
Cylindrical Capacitor
r
![Page 9: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/9.jpg)
9
rLEEA 2
r
rkE
12
inkQ4
LQin
Lk4
![Page 10: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/10.jpg)
10
rkE
12
2
1
R
REdrV 2
1
12
R
Rdrr
k 2
1ln2
R
Rrk
1
2ln2R
RkV
V
QC
LQ
V
L 12ln2 RRk
L
12ln2 RRk
L
12ln
2
RR
LC o
![Page 11: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/11.jpg)
11
Work done in Charging a Capacitor
= (Q)(Vavg)
![Page 12: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/12.jpg)
12
Q = VC Vavg = ½ Q/C
Work = (Q) x (½ Q/C)= ½ Q2/C
= area under curve
22
2
1
2
1
2
1CVQV
C
QU
![Page 13: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/13.jpg)
13
Ad
CV
volume
energyue
221
Energy Density Inside a Capacitor
Ad
dCE 2221
Ad
dE
d
A o22
21
221 Eu oe
Ex: Lab Capacitor, C = 1F, V = 6V, vol.=2x10-5 m3.
SI Unit: [J/m3]
36335
221
/10/000,900102
0.60.1mJmJ
mx
VFue
31033
8
/105.3104
104.1mJx
mx
Jxugasoline
about 35,000 higher than capacitor
![Page 14: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/14.jpg)
14
Capacitors in “Parallel” Arrangement
CVQ
""12 VVVV BA
eqBA QQQ
BA QQ VCVCVC eqBA
eqBA CCC
Ex. FFFCeq 18126
![Page 15: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/15.jpg)
15
eqBABA C
Q
C
Q
C
QVV
Capacitors in “Series” Arrangement
C
QV eqBA QQQ
Q = 0eqBA CCC
111
12
1
6
11
eqCEx.
FCeq 4
![Page 16: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/16.jpg)
16
equivalent value?
![Page 17: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/17.jpg)
17
DielectricConstant K
• reduces E and V (E = Eo/K)
• C = KCo
• C = Capacitance with Dielectric
• Co = “Empty” Capacitor
![Page 18: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/18.jpg)
18
Ex. K’s
• vacuum: 1 exactly
• air: 1.00059
• paper: 3.7
• water: 80
• barium titanate: 1200
• potassium tantalate niobate (0 °C): 34,000
![Page 19: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/19.jpg)
19
Supercapacitors
• porous structure
• surface areas much greater
• charge separation distance < 1 nm
• very high capacitance
![Page 20: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/20.jpg)
20
Batteries
slow/special charging
limited # cycles with decreasing utility
short life
high energy density
poor low temp. performance
Capacitors
simple/fast charging
over 500,000 cycles at 100%
10 to 12 year life
low energy density
good low temp. perf.
![Page 21: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/21.jpg)
21
Summary
• Electrostatic potential energy
• Capacitance: field, energy, voltage, charge
• Capacitors in circuits
• Dielectrics
• /
![Page 22: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/22.jpg)
22
![Page 23: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/23.jpg)
23
![Page 24: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/24.jpg)
24
![Page 25: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/25.jpg)
25
![Page 26: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/26.jpg)
26
![Page 27: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/27.jpg)
27
![Page 28: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/28.jpg)
28
![Page 29: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/29.jpg)
29
ji ij
ji
r
qkq
2
1
a
kq
a
kq
a
kq
a
kq
a
kq
a
kq 222222
222
1
a
kq
a
kq
a
kq
a
kq
a
kq
a
kq 222222
222
1
qqq ji
aarij 2,
Example with:
![Page 30: 1 24 Electrostatic Potential Energy. 2 3 4 Example as shown:](https://reader035.fdocuments.us/reader035/viewer/2022070400/56649f125503460f94c2657d/html5/thumbnails/30.jpg)
30
Rolled Parallel-Plate Capacitor (Can Shape)