MUATAN dan MEDAN LISTRIK

Yohanes Edi Gunanto

Muatan Listrik

Two types of charges exist They are called positive and negative Named by Benjamin Franklin

Like charges repel and unlike charges attract one another

Nature’s basic carrier of positive charge is the proton Protons do not move from one material

to another because they are held firmly in the nucleus

Attractive force Repulsive force

Asal muatan Atoms consist of a nucleus

containing positively charged protons.

The nucleus of an atom is surrounded by an equal number of negatively charged electrons.

The net charge on an atom is zero.

An atom may gain or lose electrons, becoming an ion with a net negative or positive charge.

Polar molecules have zero net charge but their charges are unevenly distributed in space (e.g. water).

Nuclear diameter ~ 10-15 m (femtometer)

Atomic diameter ~ 10-9 m (nanometer)

Classes of Materials

CONDUCTORS are materials in which charges may move freely (e.g. copper).

INSULATORS are materials in which charges cannot move freely (e.g. glass).

SEMICONDUCTORS are materials in which charges may move under some conditions (e.g. silicon).

Bagaimana muatan diukur ?

elektroskope / elektrometer

Hukum Coulomb

212

2112

||||||

rqqk

F

2q12F1q 21F

12r

For charges in aVACUUM

2

291099.8

CmNk =

2

212

00

1085.8with 41

mN

Ck

Quantum of Electric Charge

Electric charge is quantized. The smallest possible unit is the charge on one electron or one proton:

e= 1.602 x 10-19 Coulombs No smaller charge has ever been detected in an

experiment.

Catatan kecil:Ahli Fisika partikel elementer (juga ahli Fisika energi tinggi, 1963) berteori bahwa ada partikel yang lebih kecil, disebut quark, yang mempunyai muatan 2/3 e atau 1/3 e.

Deteksi eksperimen secara langsung pada partikel-partikel ini sulit dimungkinkan karena secara teori tidak ada quark bebas.

Principle of Superposition

For a system of N charges q1, q2, q3, …, qN, the resultant force F1 on q1 exerted by charges q2, q3, …, qN is:

NFFFF 113121

• Each charge may be considered to exert a force on q1 that is independent of the other charges

present.

Contoh soal :

Hitung besar gaya listrik pada sebuah elektron dalam atom hidrogen (karena tertarik oleh sebuah proton, Q2 = e). Jarak rata-rata proton-elektron: 0,53 x 10-10 m

Jawab:

Q1 = - e = - 1,6 x 10-19 C

Q2 = e = 1,6 x 10-19 C

r = 0,53x10-10 m

tanda negatif berarti attraktif.(Kemana arah gaya? gaya pada elektron mengarah ke proton)

Hitung gaya (net gaya) yang bekerja pada Q3 dari gambar berikut karena dua muatan yang lain.

Electric Field

Electric Field Line Electric Field Line PatternsPatterns Point chargePoint charge The lines radiate The lines radiate

equally in all equally in all directionsdirections

For a positive For a positive source charge, source charge, the lines will the lines will radiate outwardradiate outward

Electric Field Line Electric Field Line PatternsPatterns For a negative For a negative

source charge, source charge, the lines will the lines will point inwardpoint inward

Electric Field Line Electric Field Line PatternsPatterns An electric An electric dipoledipole

consists of two consists of two equal and equal and opposite chargesopposite charges

The high density The high density of lines between of lines between the charges the charges indicates the indicates the strong electric strong electric field in this regionfield in this region

Electric Field

The ELECTRIC FIELD E is defined in terms of the electric force that would act on a positive test charge q0 :

N/Cin 0q

FE e

The electric force on a positive test charge q0 at a distance r from a single charge q:

rr

qk

q

FE e ˆ

20

rr

qqkFe ˆ

20

• The electric field at a distance r from a single charge q:

EqFe

0

Electric Field due to a Group of Charges:

ii i

i rr

qkE ˆ

2

0i tofromr unit vecto a is ˆ q qri

Example Problem

Four point charges are at the corners of a square of side a as shown.

Determine the magnitude and direction of the electric field at the location of q.

What is the resultant force on q?

2q q

4q3q

a

a a

a

Electric Field ON axis of dipoleElectric Field ON axis of dipole

EEE :ionSuperposit

2

2

a

x

kqE

Pa x

-q +qa x

-q +q

2

2

a

x

kqE

22

2

1

2

1

ax

ax

kqE 222

4

2

a

x

xakq

222

222

4

2

4

2

a

x

kpx

ax

xakqE p = qa

“dipole moment”-- VECTOR - +

What if x>> a? (i.e. very far away)

34

22

x

kp

x

kpxE 3r

pE

E~p/r3 is actually true for ANY point far from a dipole (not just on axis)

Electric Dipole in a Uniform FieldElectric Dipole in a Uniform Field Net force on dipole = 0;

center of mass stays where it is.

Net TORQUE INTO page. Dipole rotates to line up in direction of E.

| | = 2(QE)(d/2)(sin = (Qd)(E)sin

p| E sin

= |p x E| The dipole tends to

“align” itself with the field lines.

Distance between charges = d

Electric Field from Continuous Charge Distributions

22

r

dQkdEE

r

dQkdE

If a total charge Q is distributed continuously, it may be sub-divided into elemental charges dQ, each producing an electric field dE:

02

02 4

1 ˆ

4

1ˆ

πεkr

r

dQr

r

dQkE

ε0 = permittivity of free space

Uniform Charge DistributionsUniform Charge Distributions

Volume Charge Density:Volume Charge Density: ρ=Q/Vρ=Q/V Surface Charge Density:Surface Charge Density: σ=Q/Aσ=Q/A Linear Charge Density:Linear Charge Density:λ=Q/lλ=Q/l

Q/L

Q/A Q/V

Example: Field on Bisector of Example: Field on Bisector of Charged RodCharged Rod Uniform line of charge +Q

spread over length L What is the direction of

the electric field at a point P on the perpendicular bisector?

(a) Field is 0. (b) Along +y (c) Along +x• Choose symmetrically

located elements of length dx• x components of E cancel

q

L

a

P

o

y

x

dx dx

Line Of Charge: Field on bisectorLine Of Charge: Field on bisector 22 xad

Lq

2

)(

d

dqkdE

Q

L

a

P

ox

dE

dx

d

Distance

Charge per unit length

2/322 )(

)(cos

xa

adxkdEdEy

2/122 )(cos

xa

a

2/

2/2/322 )(

L

Ly

xa

dxakE

2/

2/222

L

Laxa

xak

224

2

Laa

Lk

What is E very far away from the line (L<<a)?What is E if the line is infinitely long (L >> a)?

a

k

La

LkEy

222

A rod of length l has a uniform positive charge per unit length λ and a total charge Q. Calculate the electric field at a point P that is located along the long axis of the rod and a distance a from one end.

Start with

20

20 4

1

4

1

x

dx

x

dqdE

dxdq

Then :

al

a

al

a

al

a xx

dx

x

dxE

1

444 02

02

0

)(4

11

4

1

00 ala

Q

alal

QE

Finalize

l => 0 ?a >> l ?

TERIMA KASIH