전기퍼텐셜과퍼텐셜에너지 -...

Department of Physics

전기퍼텐셜과 퍼텐셜에너지

Department of Physics

電位= (정)전기퍼텐셜; electrical potential

1

2

Department of Physics

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

Department of Physics

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

Department of Physics

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.

Department of Physics

공간의 전기적특성을 나타냄

전기 퍼텐셜≡전위(電位)

0

0 00

( )( ) ( ) () q

q

U rU r q V r V r

q

⋅⋅

≡

⇔

⋅

퍼텐셜에너지

Department of Physics

p.78124.4 Equipotential Surfaces:

전기장 등전위면

⋅

Department of Physics

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

⋅

Department of Physics

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)

Department of Physics

(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

Department of Physics

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

Department of Physics

p.801 보기문제

C 점에서의 전기퍼텐셜과 전기장은 ?

p.801

Department of Physics

(24-8절)

0

14

dqdV

rpe=

p.802

>> r d

전위를 직접 계산하기

Department of Physics

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

Department of Physics

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!!

Department of Physics

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

Department of Physics

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

Department of Physics

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 :

Department of Physics

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

Department of Physics

"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

Department of Physics

축전기와 전기용량

Department of Physics

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.

Department of Physics

V

q

O

q = CV

Department of Physics

n

p.827

Department of Physics

[pF/m] 85.8][F/m 1085.8

]m/N[C 1085.812

22120

Department of Physics

2. 원통형 축전기

S n

Department of Physics

3. 구형(spherical) 축전기

Sn

Department of Physics

iC C병 렬 등 가

Department of PhysicsiC C

직렬등가

Department of Physics

보기문제, P. 836 축전기로 다른 축전기 충전하기

0 0 11

2 1 2

1 2

11 1

q q CqC C CC C

Department of Physics

전기장에 저장된 에너지:축전기 “충전”: “에너지 저장하기”

p.837

---

--

+++++

dq'

q'-q'

V'

q'q

V' V

Charge

VoltageO

A

B

Department of Physics

보기문제, p. 839

Department of Physics

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

Department of Physics

25-6,7,8절

Department of Physics

p. 826

Department of Physics

Department of Physics

Department of Physics

Department of Physics

Department of Physics

p. 843

Department of Physics

Department of Physics

Department of Physics

Dielectric and Gauss’ Law

Department of Physics

2 22

00 0

0 00 0

1 2 2 2(

')

Q QQU UC

UC

UC k k

= = = <=

Department of Physics

2 220 0 0 0

0 0 0( )

2 2'

2UC V C VC U UVU k

k= = >= =

Department of Physics

Department of Physics

보기문제: