전기퍼텐셜과퍼텐셜에너지 -...
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전기퍼텐셜과 퍼텐셜에너지
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電位= (정)전기퍼텐셜; electrical potential
1
2
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정전기력: 보존력 정전기적 퍼텐셜에너지
Electric potential (전위) V : 단위 양전하 당 전기퍼텐셜에너지
0qq
전위차 (전압)
( )f
f ii
W F ds U U U
unit positive charge = +1 C
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대전된 모든 입자들이 무한히 멀리 떨어져 있는 경우를“대전된 입자계의 기준 상태”(=퍼텐셜에너지가 0인 상태)로 잡자.
-- set Ui = 0 at infinity as our reference potential energy
Here W∞ is the work done by the electric field on a charged particle as that particle moves in from infinity to point f.
Unit for the electric field, E :
Energy unit
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U
W
모든 입자들이 서로 무한히 멀리 떨어져 있을 때의 퍼텐셜에너지= 0
Wq
0qq
p.791
대전된 모든 입자들이 무한히 멀리 떨어져 있는 경우를“대전된 입자계의 기준 상태”(=퍼텐셜에너지가 0인 상태)로 잡자.
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공간의 전기적특성을 나타냄
전기 퍼텐셜≡전위(電位)
0
0 00
( )( ) ( ) () q
q
U rU r q V r V r
q
⋅⋅
≡
⇔
⋅
퍼텐셜에너지
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p.78124.4 Equipotential Surfaces:
전기장 등전위면
⋅
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f
iif
if
f
i
sdEVV
VVqsdEqW
sdEqsdFdW
)( 00
0
퍼텐셜의 “기준점”
p.796 전기장에서 퍼텐셜 찾아내기
for infinitesimal disp lacemen t dV E dr dr
⋅
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보기문제 24-2(b) p.798
(cos 45 )
(cos 45 )
(cos 45 )cos 45
f fc
f ii i cf f
c cf
c
V V E ds E ds E ds
E ds E ds
E
d
s
dE
E
d
양(+)의 시험전하를 i에서 f로 이동시킴으로써계산하기
f iV V
참고: 보기문제 24-2 (a)
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(24-6절)
: ) ?0 (V rq 질문 인경우의
p.798
1. 점전하 q가 만드는 전기 퍼텐셜
.q r R P r 0시험전하 를 인 점 에서 위치로 옮기는 경우를 생각하자
전하분포와 전기퍼텐셜
14
⋅ cos0
⇒ 0 41
41 1
4
14
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0q
1q2q
30 1 0 2 1 2
0 0 01 02 12
1 14 4
i j
i j ij
q q q q q q q qUr r r r
0q1q
2qx
14
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p.801 보기문제
C 점에서의 전기퍼텐셜과 전기장은 ?
p.801
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(24-8절)
0
14
dqdV
rpe=
p.802
>> r d
전위를 직접 계산하기
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연속 전하 분포에 의한 전위
dxdqrdqdV ;
41
0
2 2 1/20 0
14 ( )
L
V dV dxx d
(24-9절)p.803
2
2 2
tan sec ; ;1 tan s ec
x d dx d d
2 20
0
2 2
0
2 2
0
[ln( )]4
[ln( ) ln ]4
ln[ ]4
Lx x d
L L d d
L L dd
숙제
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Ring of Charge
2 2 1/ 20
2 2 1/ 20
14 ( )1
4 ( )
dsdVz RqV
z R
Disk of Charge
2 2 1/20 0
22 2 1/2
' 02 2 1/20 00
2 2
0
1 2 ' '4 ( ' )
( ' ) 2( ' ) |4 ( ' ) 4
( )2
R
RRR
R dRdVz R
d R z Rz R
V z R z
(2 ')( ')dq R dR
p.805
/ (2 )q R
각자 노트에 직접해 보기!!
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전기퍼텐셜에서 전기장 찾아내기 P. 805
0
0 0 cos
dW q dV
q E ds q E ds
or cos sdVds
dVEds
E
( , , ) , , x y zV V VV V x y z E E Ex y z
⋅
고전위
저전위
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P. 807 보기문제
Disk of Charge
2 2 1/20
2 2
0
1 2 ' '4 ( ' )
( )2
R dRdVz R
V z R z
2 201
2zV zEz z R
? ?x yV VE Ex y
전기퍼텐셜에서 전기장 찾아내기
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2
For , 01For ,
4 o
r R Eqr R Er
R qElectric Field and Electric Potential for a conducti ( of radius and charge Spherical Shen lg l 도체 공껍질;구각)
1For , 4
1For , 4
o
o
qr R VRqr R Vr
R
the the electric field and electric potential
are identical to that of a equal to net conduct
Outside spherical conductor
at the center of the sphereor c
,
point charge .
the and placedarg
h e
Note :
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conductor
path
A
B
0E
All the points on a conductor have the same potential.
'' '' (either on the surface or inside)
Potential of an isolated conductor:
Consider two points A and B on or inside a conductor.
B
B AA
V V E ds
"A conductor is an equipotential surface."
(
,
)등퍼텐셜면 등전위면
P 810
"the electrostatic field inside a condWe know uctor t is zero."hat E
The integral and for any two points on or inside
the conductor.
=0B
B AA
E d s V V
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"Surface of a conductor is an ." equipotential surfaceelectric field "equipotential l su rfain cees " " s".
All the charges of the conductor reside on the surface
and arrange themselves so that , 0in outo
E E
Isolated conductor in an external electric field
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축전기와 전기용량
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축전기; capacitor; condenser
가장 단순한 소자 요소
p.826
However, we refer to the charge of a capacitor as being q, the absolute value of these charges on the plates.
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V
q
O
q = CV
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n
p.827
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[pF/m] 85.8][F/m 1085.8
]m/N[C 1085.812
22120
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2. 원통형 축전기
S n
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3. 구형(spherical) 축전기
Sn
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iC C병 렬 등 가
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직렬등가
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보기문제, P. 836 축전기로 다른 축전기 충전하기
0 0 11
2 1 2
1 2
11 1
q q CqC C CC C
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전기장에 저장된 에너지:축전기 “충전”: “에너지 저장하기”
p.837
---
--
+++++
dq'
q'-q'
V'
q'q
V' V
Charge
VoltageO
A
B
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보기문제, p. 839
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보기문제, P. 839
대전된 고립 도체 공
04C R2 2
0
2 8q qUC R
(a) 도체공에 저장된 정전기적인 퍼텐셜에너지
(b) 도체공 표면 에너지 밀도
20
14
qER
표면 전기장
22
0 2 40
1 1 2 32
qu ER
qR
4
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25-6,7,8절
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p. 826
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p. 843
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Dielectric and Gauss’ Law
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2 22
00 0
0 00 0
1 2 2 2(
')
Q QQU UC
UC
UC k k
= = = <=
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2 220 0 0 0
0 0 0( )
2 2'
2UC V C VC U UVU k
k= = >= =
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