Kuliah 4: Potensial listrikKuliah 4: Potensial listrik

"The world little knows how many of the thoughts and theories which have passed through the mind of the scientific investigator have been crushed in silence and secrecy by his own severe criticism and adverse examination; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realized."

--Michael Faraday

Michael Faraday (1791-1867)

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

2

Potensial listrik: Potensial listrik:

Gaya Elektrostatika Gaya Gravitasi

Medan dan energi Medan dan energi

Medan listrik seragamMedan listrik seragam:

PE=qEdPE=qEd

Medan listrik seragam :Medan listrik seragam :

PE = mghPE = mgh

Energi potensial: muatan titikEnergi potensial: muatan titik Energi potensial: massa titikEnergi potensial: massa titik

Potensial: Muatan titikPotensial: Muatan titik Potensial: Massa titikPotensial: Massa titik

r

mmGPE 21

r

qqkPE 21

b

a

ab ldFUU

b

a

ab ldFUU

r

mGpotentialGrav .

r

qkV

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

3

B

ABAAB dWUUU lF

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

4

1. Ua = Ub > Uc = Ud 2. Ua = Uc > Ub = Ud 3. Ub = Ud > Ua = Uc 4. Ud > Ub = Uc > Ua 5. Ud > Uc > Ub > Ua

r

qqU 21

0

21 q

4

1

r

kq

Energi potensial listrikEnergi potensial listrik

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

5

Potensial listrikPotensial listrik

r

kQV

r

kQ

r

kQdr

r

kQVV

r

kQE

ldEVV

ldq

F

q

U

q

U

ldFUU

ab

b

a

ab

b

a

ab

b

a

ab

b

a

ab

infinityat 0V If

)(22

000

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

6

Grafik VGrafik V

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

7

Permukaan ekuipotensialPermukaan ekuipotensial

r

qqU

r

q

21

0

21

0

q

4

1

r

kq

4

1

r

kqV

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

8

Permukaan ekuipotensialPermukaan ekuipotensial

Two positive charges repelling each other (weak field in between)

Two unlike charges attracting each other (strong field in between and weak field outside)

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

9

Urutkan potensial terbesar --terkecil

1. ∆V12 > ∆V13 = ∆V23 2. ∆V13 > ∆V12 > ∆V23 3. ∆V13 > ∆V23 > ∆V12 4. ∆V13 = ∆V23 > ∆V12 5. ∆V23 > ∆V12 > ∆V13

Potensial listrik pada muatan titikPotensial listrik pada muatan titik

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

10

Bola bermuatan: E and VBola bermuatan: E and V

E = 0 pada bola bermuatan

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

11

Permukaan ekuipotensialPermukaan ekuipotensial

E = 0

V = const

rkVr

rkV

r

qkV

4

4 2

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

12

Contoh 2: E dan V oleh muatan titikContoh 2: E dan V oleh muatan titik

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

13

Jawab :Jawab :

m

Ck

m

CkV

m

Ck

m

CkV

r

kQ

r

kQV

VVV

A

A

QAQAA

QAQAA

6.0

)1050(

6.0

)50(

3.0

)50(

6.0

)50(

6

2_

2

1_

1

__ 21

04.0

)50(

4.0

)50(2_

2

1_

1

__ 21

B

B

QBQBB

QBQBB

Vm

Ck

m

CkV

r

kQ

r

kQV

VVV

r

qkV

Physics 102 Section 202 Copyright by Dr. Marina Milner-Bolotin

14

Jawab :Jawab :

Ax

Ay

AyAxA

yA

xA

yQAyQAyA

xQAxQAxA

QAQAA

E

E

EEE

m

Ck

m

CkEy

m

CkEx

EEEy

EEEx

EEE

)tan(

)sin(6.0

)50(

3.0

)50(:

0)cos(6.0

)50(:

:

:

22

22

2

__

21

21

21

y

x

EQ2

EQ1

EE

EE

EQ2

EQ1