Gaya Coulomb II

7/25/2019 Gaya Coulomb II

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Todays agenda:

The electric feld.You must be able to calculate the orce on a charged

particle in an electric feld.

Electric feld due to a point charge.You must be able to calculate electric feld o a pointcharge.

Motion o a charged particle in a uniorm electric feld.You must be able to solve or the trajectory o a chargedparticle in a uniorm electric feld.

The electric feld due to a collection o point charges.You must be able to calculate electric feld o acollection o point charges.

The electric feld due to a continuous line o charge.You must be able to calculate electric feld o acontinuous line o charge.


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like charges repel

unlike charges attract

charges can move but charge is conserved

There are two kinds of charge. + -

Static Electricity

Properties of charges

Electric Charge


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Although there are two kinds of charged particles in an

atom, electrons are the charges that usually move

around.

A proton is roughly 2000 times more massive than an

electron.

The charge of an electron is e = 1.!10

"1#

coulom$s.

The charge of a proton is %e = %1.!10 "1#coulom$s.

&harges are quantized'come in units of e= 1.!10"1#&(.

+ -


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)ranklin*s e!periments showed him that there were

two +kinds of charge, which he named +positive and

+negative. -ore than a century later we learned thatnegative charges are associated with electrons, and

positive charges with protons


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Sisir melalui rambutElektron-elektron digerakkan secara mekanik darirambut dan diam pada sisir dan selanjutnya anda akan

mendapatkan bahwa sisir menarik potonngan kertas-kertas kecilBila suatu material mempunyai siat dengan cara ini !maka

material dikatakan menjadi dimuati secara listrik

" electrically charged / electrifed #


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eorang ibu dan anaknya sedang menikmati pengaruh pengisian muatistrik ke dalam tubuh mereka. Setiap helai rambut di kepala merekauatan listrik dan menghasilkan gaya tolak menolak dengan helai ra

ainnya. %kibatnya rambut mereka berdiri ! seperti yang anda lihat.


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bar "a# Batang karet bermuatan negati digantung bebas ditarik oleh batangkaca bermuatan positi. "b# batang karet bermuatan negati ditolakoleh batang karet lainnya bermuatan negati

serangkaian percobaan sederhana ! ditemukan bahwa ada dua jenis muatandiberi nama muatan positi dan negati oleh Benyamin (ranklin " )*,-)*

ktron-elektron diidentikasi bermuatan negati ! sedangkan proton-protonuatan positi. /erikasi adanya dua jenis muatan itu ! seperti pada &ambar

Berdasarkan kesepakatan yang diusulkan oleh (ranklin 0aret

digosok kain sutra ! disebut bermuatan negati ! sedangkan0aca dogosok kain sutra!


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Law of conservation of charge/ the net amount of electric charge produced in any

process is ero. (Not on your starting euation sheet! but a fact that you can use anytime"#

1asil eksperimen : 2uatan listrik selalu kekal dalam sistem terisolasi'roses pengaliran listrik " elektrikasi # adalah perpindan muatan darbenda yang satu ke benda lainnya.

Salahsatu benda mendapat sejumlah muatan negati ! sementara blainnya mendapat sejumlah muatan positi dengan jumlah yang sam3ontoh : 0aca digosok denga kain sutra : 0ain sutra mendapat muanegati dengan jumlah yang sama dengan muatan positi pada kaca


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%plikasi 1ukum 3oulomb

). $ensa kontak! etalkon mempunayai siat tarik menarik

denganair mata! maka akibatnya lensa tidak dianggap benda

asing oleh mata.4. Bahan kosmetik : cat rambut

Touch pads, capacitance keyboards,cathode-ray tubes, liuid crystal displays, and electrostaticprinters.!n medical "ork, diagnosis is oten carried out "ith the aid oelectrostatics, as incorporatedin electrocardiograms, electroencephalograms, and otherrecordings o organs "ith

electrical activity including eyes, ears, and stomachs. !n industry,electrostatics is appliedin a variety o orms such as paint spraying, electrodeposition,electrochemical machining,and separation o fne particles. Electrostatics is used inagriculture to sort seeds, directsprays to plants, measure the moisture content o crops, spincotton, and speed baking o


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'roses induksi

# Bola logam netral ! banyaknya muatan positi sama dengan muatan negat# Elektron-elektron pada bola netral di redistribusi " terdistribusi ulang

bila batang karet bermuatan negati ditempatkan dekat dengan bol

# Bila bola ditanahkan (grounded ) ,beberapa elektronnya meninggalkanbola lewat kawat tanah. " ground wire #

# Bila sambungan kawat tanah dilepas! bola akan mempunyai kelebihanmuatan positi yang terdistrubusi tidak merata

# Bila batang karet diambil! sisa elektron-elektron yang ada di redistribusi secara tidak merata dan ada distribusi merata netto muatan positi pad bola


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1ukum 3oulomb 5an 6ntensitas 2edan

1ukum 3oulomb adalah hukum eksperimental!

diormulasi pada tahun )*78 oleh (renchcolonel! 3harles %ugustin de 3oulomb. 6amenunjukkan adanya gaya antara muatan titikyang satu dengan muatan lainnya

0ontribusi 3oulomb : ")*9,-)7,#). Elektrostatika dan magnetstatika4. 0ekuatan berbagai bahan serta menentukan gaya gaya

yangmempengaruhi benda dalam sinar

9. 5alam bidang ergonomi! membeikan dasar-dasarpemahaman bagaiman manusia dan hewan melakukan usaha yang

optimal.


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1ukum 3oulomb 5an 6ntensitas 2edan

1ukum 3oulomb menyatakan bahwagaya Fantara dua muatan titik Q)dan

Q4adalah :

%epanjang garis penghubung muatannya &erbanding lurus terhadap hasil kalimuatan Q#dan Q$ &erbanding terbalik terhadap jarak antara

muatan pangkatdua ' ketidak pastian bbrp persen saja.

(ercobaan modern ketidak pastian hampir satu per #)pangkat #* +


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Secara matematik dinyatakan!


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&ra;itational (ields

1 2

2

12

m mF =G , attractiveG r

r

GFg(r) =m

r r

is the local gra;itational eld. kg! directed towards the center o the earth.

g(r)

?nits o g areactually =>kg@


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arison o Strength o Electromagnetic ;s. &ra;itati(orce

2

21

r

mmGFG=

2

21

04

1

r

qqFEM

=

=

===

2272

2

11

219

2

212

2

2

2

2

2

2

)1067.1)(1067.6(

)106.1(

)1085.8(4

1

4

1

4

1

KgKgNm

C

Nm

C

Gm

e

rmG

r

e

F

F

p

o

p

o

G

EM

36102.1 =

G

EM

F

FElectromagnetism is much stronger@

mpA).,*)-4*0g

e A).,)-)3

CoA7.78)-)434>"=m4#

&A,.,*)-))"=m4#>0g4


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'D


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3oulombs $aw Fuanties the interactionbetween charged particles.

+ -

oulombs /a"The &ig (icture

G) G4

r)41 2

2

0 12

q q1F = ,12 4 r

3oulombs $aw was disco;ered throughdecades o eperiment.


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%olving (roblems !nvolving oulombs/a" and 0ectorsou may wish to review vectors 'on your own(.

y

G4A+83

G9A+,83

G)A-7,3

84 cm

,+cm9+cm

A9H

E$ample% &alculate the net electrostatic force oncharge 3due to the charges 1 and 2.


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y

G4A+83

G9A+,83

G)A-7,3

84 cm

,+cm9+cm

A9H

(9)

(94

%tep # 1iagram


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1 2

2

12

q q

F k12 r=

y

G4A+83

G9A+,83

G)A-7,3

84 cm

,+cm9+cm

A9H

(9)

(94

%tep $ %tarting Euation


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3 22

32

F k ,32 r

re!"#$ive

=r

3 2

2

32

F k32,% r

=

F 032,& = 'from diagram(

&an you put num$ers in at this point4 56 for this pro$lem. ou would get )32,y= 330 7

and )32,!= 0 7.

y

G4A+83

G9A+,83

G)A-7,3

84 cm

r9)A,+cm

r

94A9+cm

A9H

(9)

(94

%tep 2 3eplace 4eneric 5uantities by%pecifcs


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3 1

2

31

F k ,31

rattractive

=r

3 1

231

F k c'$31, & r= +

&an you put num$ers in at this point4 56 for this pro$lem. ou would get )31,!=

%120 7 and )31,y

= "80 7.

'" sign comes from diagram(3 12

31

F k $i31, % r

=

'% sign comes from diagram(

y

G4A+83

G9A+,83

G)A-7,3A9H

(9)

(94

%tep 2 'continued+

r

94A9+cm r

9)A,+cm

84 cm


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)3!= )31,!% )32,!= 120 7 % 0 7 = 120 7

)3y= )31,y% )32,y= "80 7 % 330 7 = 20 7

ou know how to calculate the magnitude )3and the angle $etween )3and the !"a!is.

'9f not, holler:(

(9The net force is the vector

sum of all the forces on 3.

y

G4A+83

G9A+,83

G)A-7,3

84 cm

,+cm9+cm

A9H

(9)

(94

%tep 2 omplete the Math


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9 did a sample &oulom$*s law calculation

using three point charges.

;ow do you apply &oulom$*s law

to o$


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o

enc

SQadE=

0=

S

adB

dt

dldE

=

encoIldB =

o

E=

0= B

t

BE

=

t

EJB ooo

+=

2awells EFuations

&ausss $aw

(aradays $aw

%mperes $aw

E/ET36%T7T! 8!E/1%


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E/ET36%T7T! 8!E/1%

Medan Elektrostatis ditimbulkan oleh distribusimuatan statis.7plikasinya sangat luas Electric po"er transmission, 9-ray machines,

and lightning protection berhubunganerat dengan medan listrik dan memerlukanpemahaman elektrostatika untukmerencanakan peralatan yg cocok.

(iranti :piranti yang digunakan pada in solid-stat electronics beroperasi berbasis padaelektrostatika. Misalnya 3esistor, kapasitordan piranti akti feld e;ect transistor . 1lmpiranti akkti gerakan elektron dikontrol oleh

medan elektrostatis .

(iranti-piranti yg bekerja berbasis elektrostatisadalah

Touch pads, capacitance keyboards,

cathode-ray tubes, liuid crystal displays, and electrostatic printers.!n medical "ork, diagnosis is oten carried out "ith the aid oelectrostatics, as incorporatedin electrocardiograms, electroencephalograms, and otherrecordings o organs "ithelectrical activity including eyes, ears, and stomachs. !n industry,electrostatics is appliedin a variety o orms such as paint spraying, electrodeposition,


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I7

?lectrostatics/

)undamental postulates of electrostatics and&oulom$@s aw

?lectric field due to a system of discrete charges ?lectric field due to a continuous distri$ution of charge Bauss@ aw and applications ?lectric Cotential &onductors in static electric field Dielectrics in static electric fields ?lectric )lu! Density, dielectric constant

Eoundary &onditions &apacitor and &apacitance 7ature of &urrent and &urrent Density


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I

?lectrostatics/

Fesistance of a &onductor

Goule*s aw Eoundary &onditions for the current density The ?lectromotive )orce The Eiot"Havart aw


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8

-agnetostatics/

Ampere*s )orce aw-agnetic TorIue-agnetic )lu! and Bauss*s aw for -agnetic )ields-agnetic Jector Cotential

-agnetic )ield 9ntensity and Ampere*s &ircuital aw-agnetic -aterialEoundary &onditions for -agnetic )ields?nergy in a -agnetic )ield-agnetic &ircuits9nductance


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8)

1ynamic 8ields:

(aradays $aw and induced em Transormers 5isplacement 3urrent Time-dependent 2awells eFuations andelectromagnetic wa;e eFuations

Time-harmonic wa;e problems! uniorm plane wa;es inlossless media! 'oyntings ;ector and theorem

?niorm plane wa;es in lossy media ?niorm plane wa;e transmission and reJection onnormal and obliFue incidence

E l El t ti


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84

Eamples o Electromagneticelds

Electromagnetic felds Solar radiation $ightning Dadio communication 2icrowa;e o;en

$ight consists o electric and magnetic elds. %nelectromagnetic wa;e can propagate in a

;acuum with a speed ;elocity c=2.998x10

8

m/

c = !! = !re"uency (#$)= %a&elength (m)

6 7?1 8!E/1 !?TE?%!TY


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6 7?1 8!E/1 !?TE?%!TY

3oulombs law is an eperimental law ormulated in )*78 bythe (rench colonel! 3harles %ugustin de 3oulomb. 6t deals with

the orce a point charge eerts on another point charge.

Epressed mathematically!

n


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Lightp

rotectio

n


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(oto dramatik ini menangkap gambar saatSambaran petir menyambar pohon di dekat daera'edesaan. 'etir biasanya dikaitkan dengan medan

$istrik yang sangat kuat di atmosr.


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6nduksi mutan positi di permukaan tanah

Beda 'otensial'elepasan muatan> Sambaranpetir


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per tahun! di 3ibinong

%rus petir 9-7 k%! pernah terdeteksi sampai 9 k%! dengan energisatu kali sambaran 88 kKh A 88 ) 9, Ks A )7 2L


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Batas arus Pengaruh pada tubuh manusia

0 - 0,9 mA Belum merasakan pengaruh0,9 - 1,2 mA Baru terasa adanya arus listrik tapi tidak

menimbulkan kejang

1,2 - 1,6 mA Mulai terasa se akan2 ada yang merayap didalam tangan1,6 - 6,0 mA Tangan sampai kesiku merasa kesemutan6,0 - ,0 mA Tangan mulai kaku, rasa kesemutan makin bertambah1! - 1",0 mA #asa sakit tak tertahankan penghantar masih dapat dilepas1" - 20,0 mA $t%t tidak sanggup lagi melepaskan penghantar

20 - "0,0 mA &apat mengakibatkan kerusakan pada tubuh manusia"0 - 100,0 mA Batas arus yang dapat menyebabkan kematian

Batas arus yang mele'ati tubuh manusia


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Tegangan sentuh (aktu Pemutusan Maksimum

)*%lt+ rms )detik+

"0

"0 1,0 ." 0,"

90 0,2

110 0,2

1"0 0,1

220 0,0"

20 0,0!

Besar dan /ama tegangan entuh Maksimum

)3+


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6 7?1 8!E/1 !?TE?%!TY


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6 7?1 8!E/1 !?TE?%!TY

3oulombs law is an eperimental law ormulated in )*78 bythe (rench colonel! 3harles %ugustin de 3oulomb. 6t deals with

the orce a point charge eerts on another point charge.

Epressed mathematically!


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The electric feld intensity 'or electric


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The electric feld intensity 'or electricfeld strength+ E is the orce per unitcharge "hen placed in the electric feld.


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The electric eld intensity at pointr due to a point chargelocated at r=is


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Contoh Soal 4 2


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Contoh Soal 4.2

Dua muatan titik mempunyai massa sama m, muatan Q

digantung pada titik $ersama dengan pan


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Tin


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Bila M sangat kecil


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E/ET3! 8!E/1% 1


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@734E 1!%T3!&


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7northogonal system is one in "hich the coordinates aremutually perpendicular.

73TE%!7? 6631!?7TE% '9, Y, A+

P(x,y,z)

The ranges o the coordinate ;ariablesx, y, and $ are


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1!88E3E?T!7/ /E?4T@, 73E7, 7?1 06/


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!3


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The ranges o the variables are

7 vector 7 in cylindricalcoordinates can be "ritten as


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E/ET3! 8!E/1% 1


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6n a parallel plate capacitor! the electric eld eisting between the

two plates ha;ing eFual and opposite charges is gi;en by


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%pplying the cosine rule to (igureI.7!


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Tititk ' "!y!N #


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/ektor 7 dalam koordinat 0artesian


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Gaya Coulomb II

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Transcript of Gaya Coulomb II