Chapter 26 Electric Potential 第二十六章 電位. Lightning.
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Transcript of Chapter 26 Electric Potential 第二十六章 電位. Lightning.
![Page 1: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/1.jpg)
Chapter 26 Electric Potential
第二十六章 電位
![Page 2: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/2.jpg)
Lightning
![Page 3: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/3.jpg)
Just before lightning
![Page 4: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/4.jpg)
Electric potential energy
![Page 5: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/5.jpg)
Electric potential energy
f iU U U W
where W is the work done by the static electric field.
For convenience we often define
fU U W
Where is the work done by the field to move the charge particle from infinity to its current position and .
W
0U
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Electric potential
f iU U U qE s
/V U q E s
In general we have
f
i
s
sV E ds
![Page 7: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/7.jpg)
Work done by an applied force
f i appK K K W W
If ΔK = 0, then appW W q V
![Page 8: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/8.jpg)
Equipotential surfaces
Surfaces in space on which V is constant.
![Page 9: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/9.jpg)
Equipotential surfaces
If ΔV is chosen to be the same for all adjacent equipotential surfaces, then the electric filed is inversely proportional to the separations of the equipotential surfaces.
![Page 10: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/10.jpg)
Calculating the potential from the field
f
i
s
f i sV V V E ds
f
i
s
f i sV V E ds
or
Vi can be assigned to any convenient value such as 0.
![Page 11: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/11.jpg)
Potential due to a point charge
20
20
0
0 0
1ˆ
4
1
4
1( )
4
1 1( )
4 4
f
i
f
i
f
i
f
i
s
f i s
r
i r
r
i r
r
i r
if i
V V E ds
qV r dr
r
qV dr
r
qV
r
q qV
r r
0
1( )
4
qV r
r If
0
1
4ii
qV
r
![Page 12: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/12.jpg)
Potential due to a point charge
0
1( )
4
qV r
r
![Page 13: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/13.jpg)
Potential due to an electric dipole
0
1( )
4
q qV V V
r r
P
r r
p
0
( )4
r rqV
r r
If the point of interest P is far away from the dipole, then
20
cos( )
4
q dV
r
20
1 cos( )
4
pV
r
20
ˆ1( )
4
p rV
r
r̂
![Page 14: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/14.jpg)
Potential due to an electric dipole
![Page 15: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/15.jpg)
Induced dipole moment
![Page 16: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/16.jpg)
Potential due to a group of point charges
1 0
1
4
n ni
ii i i
qV V
r
Example
![Page 17: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/17.jpg)
Potential due to continuous charge distribution
0
1
4
dqdV
r
0
1
4
dqV dV
r
![Page 18: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/18.jpg)
Line of charge
2 2 1/ 200
2 2 1/ 2
00
1
4 ( )
ln( ( ) )4
l
l
dxV
x a
x x a
![Page 19: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/19.jpg)
Charged disk
2 2 1/ 200
2 2 1/ 2
00
1 (2 )
4 ( )
( )2
a
a
r drV
r x
r x
![Page 20: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/20.jpg)
Calculating the field from the potential
0 0 cosq dV q E ds
cosdV
Eds
x
VE
x
ˆ ˆ ˆ( )
E V
V V Vx y z
x y z
![Page 21: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/21.jpg)
Electric potential energy of a system of point charges
'
,
1
2 iji j
U U
0
1
4i j
ijij
q qU
r
1( )
2 i j iji j i
U q V r
![Page 22: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/22.jpg)
Potential of a charged isolated conductor
![Page 23: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/23.jpg)
Surface charge density of a conductor
1 1 11
0 1 0
1
4
Q RV
R
2 2 22
0 2 0
1
4
Q RV
R
1 1 2 2R R
![Page 24: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/24.jpg)
Electric fields near a conductor
1 1 2 2R R
1 1 0/E 2 2 0/E
1 2
2 1
E R
E R
The field strength is strongest at the point on a conductor where its local curvature of radius is the smallest.
![Page 25: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/25.jpg)
Image charge
![Page 26: Chapter 26 Electric Potential 第二十六章 電位. Lightning.](https://reader033.fdocuments.net/reader033/viewer/2022061520/56649d225503460f949f8dcf/html5/thumbnails/26.jpg)
Home work
Question ( 問題 ): 8, 15, 21
Exercise ( 練習題 ): 5, 12, 19
Problem ( 習題 ): 12, 28, 29, 37