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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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