electrostatics temp

8/10/2019 Electrostatics Temp

1/22

Contents

1 Fundamental concepts

1.1 Coulomb's law

1.2 Electric field

1.3 Gauss's law

1.4 Poisson's equation

1.5 aplace's equation

2 Electrostatic appro!imation

2.1 Electrostatic potential

3 Electrostatic ener"#

4 $riboelectric series

5 Electrostatic "enerators

% C&ar"e neutraliation
http://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Fundamental_conceptshttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Coulomb.27s_lawhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electric_fieldhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electric_fieldhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electric_fieldhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Gauss.27s_lawhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Gauss.27s_lawhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Gauss.27s_lawhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Poisson.27s_equationhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Laplace.27s_equationhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electrostatic_approximationhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electrostatic_potentialhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electrostatic_energyhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Triboelectric_serieshttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electrostatic_generatorshttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Charge_neutralizationhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Coulomb.27s_lawhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electric_fieldhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Gauss.27s_lawhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Poisson.27s_equationhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Laplace.27s_equationhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electrostatic_approximationhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electrostatic_potentialhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electrostatic_energyhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Triboelectric_serieshttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Electrostatic_generatorshttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Charge_neutralizationhttp://en.wikipedia.org/w/index.php?title=Electrostatics&printable=yes#Fundamental_concepts


2/22

Electrostatics

Electrostaticsis t&e branc& ofpsicst&at deals wit& t&e p&enomena andproperties of stationar# or slow(mo)in" *wit&out acceleration+electric c&ar"es.

,t is t&e branc& of psics w&ic& deals wit& t&e stud# of c&ar"es at rest.

-inceclassical antiquit# it &as been /nown t&at some materials suc&

asamberattract li"&twei"&t particles afterrubbin". $&eGree/word for

amber067electron was t&e source of t&e word 'electricit#'. Electrostatic

p&enomena arise from t&eforcest&at electric c&ar"es e!ert on eac& ot&er. -uc&forces are described b#Coulomb's law. E)en t&ou"& electrostaticall# induced

forces seem to be rat&er wea/ t&e electrostatic force between e.".

anelectronand aproton t&at to"et&er ma/e up adro"enatom is about

48orders of ma"nitudestron"er t&an t&e"ra)itationalforce actin" between

t&em.

Electrostatic p&enomena include man# e!amples some as simple as t&e

attraction of t&e plastic wrap to #our &and after #ou remo)e it from a pac/a"e

to t&e apparentl# spontaneous e!plosion of "rain silos to dama"e of electronic

components durin" manufacturin" to t&e operation of p&otocopiers.

Electrostatics in)ol)es t&e buildup of c&ar"e on t&e surfaceof ob9ects due to

contact wit& ot&er surfaces. :lt&ou"&c&ar"e e!c&an"e&appens w&ene)er an#

two surfaces contact and separate t&e effects of c&ar"e e!c&an"e are usuall#

onl# noticed w&en at least one of t&e surfaces &as a &i"&resistanceto electrical

flow. $&is is because t&e c&ar"es t&at transfer to or from t&e &i"&l# resisti)e

surface are more or less trapped t&ere for a lon" enou"& time for t&eir effects to

be obser)ed. $&ese c&ar"es t&en remain on t&e ob9ect until t&e# eit&er bleed off
http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Classical_antiquityhttp://en.wikipedia.org/wiki/Amberhttp://en.wikipedia.org/wiki/Triboelectric_effecthttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Coulomb's_lawhttp://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Protonhttp://en.wikipedia.org/wiki/Hydrogenhttp://en.wikipedia.org/wiki/Hydrogenhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Gravitationhttp://en.wikipedia.org/wiki/Surfacehttp://en.wikipedia.org/wiki/Charge_exchangehttp://en.wikipedia.org/wiki/Resistance_(electricity)http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Classical_antiquityhttp://en.wikipedia.org/wiki/Amberhttp://en.wikipedia.org/wiki/Triboelectric_effecthttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Coulomb's_lawhttp://en.wikipedia.org/wiki/Electronhttp://en.wikipedia.org/wiki/Protonhttp://en.wikipedia.org/wiki/Hydrogenhttp://en.wikipedia.org/wiki/Atomhttp://en.wikipedia.org/wiki/Order_of_magnitudehttp://en.wikipedia.org/wiki/Gravitationhttp://en.wikipedia.org/wiki/Surfacehttp://en.wikipedia.org/wiki/Charge_exchangehttp://en.wikipedia.org/wiki/Resistance_(electricity)


3/22

to "round or are quic/l#neutraliedb# adisc&ar"e; e.". t&e familiar

p&enomenon of a static 's&oc/' is caused b# t&e neutraliation of c&ar"e built up

in t&e bod# from contact wit& nonconducti)e surfaces.

Fundamental concepts

Coulomb's law

$&e fundamentalequationof electrostatics isCoulomb's law w&ic& describes

t&e force between twopoint c&ar"es. $&e ma"nitude of t&e electrostatic force

between two point electric c&ar"es and is directl# proportional to t&e

product of t&e ma"nitudes of eac& c&ar"e and in)ersel# proportional to t&e

surface area of a sp&ere w&ose radius is equal to t&e distance between t&e

c&ar"es;

w&ere 8is a constant called t&e)acuum permitti)it#or permitti)it# of free

space a defined )alue;

in :2s4/"(

1m


4/22

C&arles :u"ustin de Coulomb

The law

@ia"ram describin" t&e basic mec&anism of Coulomb's law. i/e c&ar"es repel eac& ot&er opposite

c&ar"es attract eac& ot&er.

$&escalar formof Coulomb's law is an e!pression for t&e ma"nitude and si"n

of t&e electrostatic force between two idealied point c&ar"es small in sie

compared to t&eir separation. $&is force *F+ actin" simultaneousl# on point

c&ar"es *q1+ and *q2+ is "i)en b#
http://en.wikipedia.org/wiki/Scalar_(mathematics)http://en.wikipedia.org/wiki/Point_chargehttp://en.wikipedia.org/wiki/File:CoulombsLaw.svghttp://en.wikipedia.org/wiki/File:Coulomb.jpghttp://en.wikipedia.org/wiki/Scalar_(mathematics)http://en.wikipedia.org/wiki/Point_charge


5/22

w&ereris t&e separation distance andkeis a proportionalit# constant. : positi)e

force implies it is repulsi)e w&ile a ne"ati)e force implies it is attracti)e.

A>B

$&eproportionalit# constantke called t&e Coulomb constant *sometimes called t&e

Coulomb force constant+ is related to defined properties of spaceand can be

calculated based on t&e speed of li"&t to be e!actl#; A?B

Coulomb's torsion balance

Coulomb's law states t&at; $&e ma"nitude of t&e Electrostatics force of

interaction between two point c&ar"es is directl# proportional to t&e scalar

multiplication of t&e ma"nitudes of c&ar"es and in)ersel# proportional to t&e

square of t&e distances between t&em.
http://en.wikipedia.org/w/index.php?title=Coulomb%27s_law&printable=yes#cite_note-6http://en.wikipedia.org/wiki/Free_space#Propertieshttp://en.wikipedia.org/w/index.php?title=Coulomb%27s_law&printable=yes#cite_note-7http://en.wikipedia.org/wiki/Torsion_balancehttp://en.wikipedia.org/wiki/File:Bcoulomb.pnghttp://en.wikipedia.org/w/index.php?title=Coulomb%27s_law&printable=yes#cite_note-6http://en.wikipedia.org/wiki/Free_space#Propertieshttp://en.wikipedia.org/w/index.php?title=Coulomb%27s_law&printable=yes#cite_note-7http://en.wikipedia.org/wiki/Torsion_balance


6/22

,n-,units t&e meter is defined suc& t&at t&espeed of li"&t in

)acuum*orelectroma"netic wa)es in "eneral+ denotedc0is

e!actl#2DD>D245? ms


7/22

w&ere is t&e separation of t&e two c&ar"es. $&is is simpl# t&e scalar definition

of Coulomb's law wit& t&e direction "i)en b# t&eunit )ector parallel

wit& t&e linefromc&ar"e toc&ar"e .

,f bot& c&ar"es &a)e t&e samesi"n*li/e c&ar"es+ t&en t&eproduct is

positi)e and t&e direction of t&e force on is "i)en b# K t&e c&ar"es repel

eac& ot&er. ,f t&e c&ar"es &a)e opposite si"ns t&en t&e product is ne"ati)e

and t&e direction of t&e force on is "i)en b# K t&e c&ar"es attract eac&

ot&er.

System of discrete charges

$&e principle oflinear superpositionma# be used to calculate t&e force on a

small test c&ar"e due to a s#stem of discrete c&ar"es;

w&ere and are t&e ma"nitude and position respecti)el# of t&e c&ar"e

is a unit )ector in t&e direction of *a )ector pointin" from

c&ar"es to +.

Continuous charge distribution

For a c&ar"e distribution aninte"ralo)er t&e re"ion containin" t&e c&ar"e is

equi)alent to an infinite summation treatin" eac&infinitesimalelement of space

as a point c&ar"e .

For a linear c&ar"e distribution *a "ood appro!imation for c&ar"e in a wire+

w&ere "i)es t&e c&ar"e per unit len"t& at position and is an

infinitesimal element of len"t&

.
http://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Scalar_multiplicationhttp://en.wikipedia.org/wiki/Scalar_multiplicationhttp://en.wikipedia.org/wiki/Linear_superpositionhttp://en.wikipedia.org/wiki/Integralhttp://en.wikipedia.org/wiki/Infinitesimalhttp://en.wikipedia.org/wiki/Unit_vectorhttp://en.wikipedia.org/wiki/Plus_and_minus_signshttp://en.wikipedia.org/wiki/Scalar_multiplicationhttp://en.wikipedia.org/wiki/Linear_superpositionhttp://en.wikipedia.org/wiki/Integralhttp://en.wikipedia.org/wiki/Infinitesimal


8/22

For a surface c&ar"e distribution *a "ood appro!imation for c&ar"e on a plate in

a parallel platecapacitor+ w&ere "i)es t&e c&ar"e per unit area at

position and is an infinitesimal element of area

For a )olume c&ar"e distribution *suc& as c&ar"e wit&in a bul/ metal+

w&ere "i)es t&e c&ar"e per unit )olume at position and is an

infinitesimal element of )olume

$&e force on a small test c&ar"e at position is "i)en b#

Graphical representation

Lelow is a "rap&ical representation of Coulomb's law w&en . $&e

)ector is t&e force e!perienced b# . $&e )ector is t&e force e!perienced

b# . $&eir ma"nitudes will alwa#s be equal. $&e )ector is t&e displacement)ector between two c&ar"es * and +.

: "rap&ical representation of Coulomb's law.
http://en.wikipedia.org/wiki/Capacitorhttp://en.wikipedia.org/wiki/File:Coulombs.pnghttp://en.wikipedia.org/wiki/Capacitor


9/22

Table of derived quantities

:tHon 1 b# 2 Particle propert# Melations&ip Field propert#

Nector

quantit#

Force Electric field

Melations&i

p

-calar

quantit#

Electric energy Electric potential

Electric field

$&eelectric field*in units of)oltsper meter+ at a point is defined as t&e force

*innewtons+ per unit c&ar"e *incoulombs+ on a c&ar"e at t&at point;

Or we can sa# a c&ar"ed ob9ect in an electric field feels a force FqE

From t&is definition and Coulomb's law it follows t&at t&e ma"nitude of t&eelectric fieldEcreated b# atest c&ar"eQis;
http://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_energyhttp://en.wikipedia.org/wiki/Electric_potentialhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Newton_(unit)http://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Test_chargehttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_energyhttp://en.wikipedia.org/wiki/Electric_potentialhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Newton_(unit)http://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Test_charge


10/22

$&e electric field produced b# a distribution of c&ar"es "i)en b# t&e

)olumec&ar"e densit# is obtained b# atriple inte"ralof a )ector function;

$&e )alue of t&e electric field depicts t&e force on a c&ar"ed particle if it entered

t&e electric field. Electric field lines "i)es t&e direction of force on a positi)e

c&ar"e in t&e electric field.

Gauss's law

Gauss' lawstates t&at t&e total electric flu! t&rou"& an# closed pot&etical

surface of an# s&ape drawn in an electric field is proportional to t&e totalelectric

c&ar"eenclosed wit&in t&e surface.

at&ematicall# Gauss's law ta/es t&e form of an inte"ral equation;

:lternati)el# in differential form t&e equation becomes

w&ere is t&edi)er"ence operator.

,npsicsGauss's law also /nown asGauss's flu theorem is a law relatin"

t&e distribution ofelectric c&ar"eto t&e resultin"electric field.

$&e law was formulated b#Carl Friedric& Gaussin 1?35 but was not publis&ed

until 1?%>.,t is one of t&e foura!well's equationsw&ic& form t&e basis

ofclassical electrod#namics t&e ot&er t&ree bein"Gauss's law for

ma"netismFarada#'s law of induction and:mpQre's law wit& a!well's

correction. Gauss's law can be used to deri)eCoulomb's lawand )ice )ersa.
http://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Triple_integralhttp://en.wikipedia.org/wiki/Triple_integralhttp://en.wikipedia.org/wiki/Gauss'_lawhttp://en.wikipedia.org/wiki/Gauss'_lawhttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Maxwell's_equationshttp://en.wikipedia.org/wiki/Classical_electrodynamicshttp://en.wikipedia.org/wiki/Gauss's_law_for_magnetismhttp://en.wikipedia.org/wiki/Gauss's_law_for_magnetismhttp://en.wikipedia.org/wiki/Gauss's_law_for_magnetismhttp://en.wikipedia.org/wiki/Faraday's_law_of_inductionhttp://en.wikipedia.org/wiki/Faraday's_law_of_inductionhttp://en.wikipedia.org/wiki/Amp%C3%A8re's_circuital_lawhttp://en.wikipedia.org/wiki/Amp%C3%A8re's_circuital_lawhttp://en.wikipedia.org/wiki/Coulomb's_lawhttp://en.wikipedia.org/wiki/Coulomb's_lawhttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Triple_integralhttp://en.wikipedia.org/wiki/Gauss'_lawhttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/Maxwell's_equationshttp://en.wikipedia.org/wiki/Classical_electrodynamicshttp://en.wikipedia.org/wiki/Gauss's_law_for_magnetismhttp://en.wikipedia.org/wiki/Gauss's_law_for_magnetismhttp://en.wikipedia.org/wiki/Faraday's_law_of_inductionhttp://en.wikipedia.org/wiki/Amp%C3%A8re's_circuital_lawhttp://en.wikipedia.org/wiki/Amp%C3%A8re's_circuital_lawhttp://en.wikipedia.org/wiki/Coulomb's_law


11/22

Equation involving E!field

Gauss's law can be stated usin" eit&er t&eelectric fieldEor t&eelectric

displacement field". $&is section s&ows some of t&e forms wit&EK t&e form

wit&"is below as are ot&er forms wit&E.

#ntegral form

Gauss's law ma# be e!pressed as;

w&ere REis t&eelectric flu!t&rou"& a closed surfaceSenclosin" an#

)olumeVQis t&e totalc&ar"eenclosed wit&inS and8is t&eelectric constant.

$&e electric flu! REis defined as asurface inte"ralof t&eelectric field;

w&ereEis t&e electric field d$is a )ector representin" aninfinitesimalelement

ofareaand S represents t&edot productof two )ectors.

-ince t&e flu! is defined as anintegralof t&e electric field t&is e!pression of

Gauss's law is called t&eintegral form.

w&ereSEis t&edi)er"enceof t&e electric field andis t&e total electricc&ar"e

densit#.

.

Equation involving "!field

Free% bound% and total charge

$&e electric c&ar"e t&at arises in t&e simplest te!tboo/ situations would be

classified as free c&ar"eTfor e!ample t&e c&ar"e w&ic& is transferred

instatic electricit# or t&e c&ar"e on acapacitorplate. ,n contrast bound
http://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_displacement_fieldhttp://en.wikipedia.org/wiki/Electric_displacement_fieldhttp://en.wikipedia.org/wiki/Electric_fluxhttp://en.wikipedia.org/wiki/Electric_fluxhttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Electric_constanthttp://en.wikipedia.org/wiki/Electric_constanthttp://en.wikipedia.org/wiki/Surface_integralhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Infinitesimalhttp://en.wikipedia.org/wiki/Infinitesimalhttp://en.wikipedia.org/wiki/Areahttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Static_electricityhttp://en.wikipedia.org/wiki/Static_electricityhttp://en.wikipedia.org/wiki/Capacitorhttp://en.wikipedia.org/wiki/File:OiintLaTeX.pnghttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_displacement_fieldhttp://en.wikipedia.org/wiki/Electric_displacement_fieldhttp://en.wikipedia.org/wiki/Electric_fluxhttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Electric_constanthttp://en.wikipedia.org/wiki/Surface_integralhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Infinitesimalhttp://en.wikipedia.org/wiki/Areahttp://en.wikipedia.org/wiki/Dot_producthttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Static_electricityhttp://en.wikipedia.org/wiki/Capacitor


12/22

c&ar"e arises onl# in t&e conte!t ofdielectric*polariable+ materials. *:ll

materials are polariable to some e!tent.+ U&en suc& materials are placed in an

e!ternal electric field t&e electrons remain bound to t&eir respecti)e atoms but

s&ift a microscopic distance in response to t&e field so t&at t&e#'re more on one

side of t&e atom t&an t&e ot&er. :ll t&ese microscopic displacements add up to

"i)e a macroscopic net c&ar"e distribution and t&is constitutes t&e bound

c&ar"e.

:lt&ou"& microscopicall# all c&ar"e is fundamentall# t&e same t&ere are often

practical reasons for wantin" to treat bound c&ar"e differentl# from free c&ar"e.

$&e result is t&at t&e more fundamental Gauss's law in terms ofE*abo)e+ is

sometimes put into t&e equi)alent form below w&ic& is in terms of"and t&e

free c&ar"e onl#.

#ntegral form

$&is formulation of Gauss's law states analo"ousl# to t&e total c&ar"e form;

w&ere RDis t&e"(fieldflu!t&rou"& a surfaceSw&ic& encloses a )olumeVandQfreeis t&e free c&ar"e contained inV. $&e flu! RDis defined analo"ousl# to

t&e flu! REof t&e electric fieldEt&rou"&S;

"ifferential form

$&e differential form of Gauss's law in)ol)in" free c&ar"e onl# states;

w&ereS"is t&edi)er"enceof t&e electric displacement field andfreeis t&e

free electric c&ar"e densit#.
http://en.wikipedia.org/wiki/Dielectrichttp://en.wikipedia.org/wiki/Electric_displacement_fieldhttp://en.wikipedia.org/wiki/Electric_displacement_fieldhttp://en.wikipedia.org/wiki/Electric_fluxhttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/File:OiintLaTeX.pnghttp://en.wikipedia.org/wiki/Dielectrichttp://en.wikipedia.org/wiki/Electric_displacement_fieldhttp://en.wikipedia.org/wiki/Electric_fluxhttp://en.wikipedia.org/wiki/Divergence


13/22

&oisson's equation

$&e definition of electrostatic potential combined wit& t&e differential form ofGauss's law *abo)e+ pro)ides a relations&ip between t&e potential R and t&e

c&ar"e densit# ;

$&is relations&ip is a form ofPoisson's equation.

aplace's equation

,n t&e absence of unpaired electric c&ar"e t&e equation becomes

w&ic& isaplace's equation.

Electrostatic potential

$&e electrostatic fieldlines !it" arro!s#of a nearb# positi)e c&ar"e $#causes t&e mobile c&ar"es in

conducti)e ob9ects to separate due toelectrostatic induction. =e"ati)e c&ar"es %lue#are attracted and

mo)e to t&e surface of t&e ob9ect facin" t&e e!ternal c&ar"e. Positi)e c&ar"es red#are repelled and

mo)e to t&e surface facin" awa#. $&ese induced surface c&ar"es are e!actl# t&e ri"&t sie and s&ape
http://en.wikipedia.org/wiki/Poisson's_equationhttp://en.wikipedia.org/wiki/Laplace's_equationhttp://en.wikipedia.org/wiki/Electrostatic_fieldhttp://en.wikipedia.org/wiki/Electrostatic_fieldhttp://en.wikipedia.org/wiki/Electrostatic_inductionhttp://en.wikipedia.org/wiki/File:Electrostatic_induction.svghttp://en.wikipedia.org/wiki/Poisson's_equationhttp://en.wikipedia.org/wiki/Laplace's_equationhttp://en.wikipedia.org/wiki/Electrostatic_fieldhttp://en.wikipedia.org/wiki/Electrostatic_induction


14/22

so t&eir opposin" electric field cancels t&e electric field of t&e e!ternal c&ar"e t&rou"&out t&e interior

of t&e metal. $&erefore t&e electrostatic field e)er#w&ere inside a conducti)e ob9ect is ero and

t&e electrostatic potentialis constant.

Lecause t&e electric field isirrotational it is possible to e!press t&e electric field

as t&e"radientof a scalar function called t&eelectrostatic potential*also /nown

as t&e)olta"e+. :n electric field points from re"ions of &i"& potential R to

re"ions of low potential e!pressed mat&ematicall# as

$&e electrostatic potential at a point can be defined as t&e amount ofwor/per

unit c&ar"e required to mo)e a c&ar"e from infinit# to t&e "i)en point.

,nclassical electroma"netism t&eelectric potential*ascalarquantit# denoted

b#&&EorVand also called t&eelectric field potentialor t&eelectrostatic

potential+ at a point is equal to t&e electric potential ener"#*measured in9oules+

of a c&ar"ed particle at t&at location di)ided b# t&ec&ar"e*measured

incoulombs+ of t&e particle. $&e electric potential is independent of t&e test

particle's c&ar"e ( it is determined b# t&e electric field alone. $&e electric

potential can be calculated at a point in eit&er a static *time(in)ariant+electric

fieldor in a d#namic *)ar#in" wit& time+electric fieldat a specific time and &as

t&e units of9oulespercoulomb or)olts.

$&ere is also a "eneralied electricscalar potentialt&at is used

inelectrod#namicsw&en time()ar#in" electroma"netic fields are present. $&is

"eneralied electric potential cannot be simpl# interpreted as t&e ratio of

potential ener"# to c&ar"e &owe)er.

Ob9ects ma# possess a propert# /nown as an electric c&ar"e. :n electric field

e!erts a force on c&ar"ed ob9ects acceleratin" t&em in t&e direction of t&e force
http://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Irrotationalhttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Work_(physics)http://en.wikipedia.org/wiki/Classical_electromagnetismhttp://en.wikipedia.org/wiki/Scalar_(physics)http://en.wikipedia.org/wiki/Scalar_(physics)http://en.wikipedia.org/wiki/Electric_potential_energyhttp://en.wikipedia.org/wiki/Joulehttp://en.wikipedia.org/wiki/Joulehttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Jouleshttp://en.wikipedia.org/wiki/Jouleshttp://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Scalar_potentialhttp://en.wikipedia.org/wiki/Electrodynamicshttp://en.wikipedia.org/wiki/Electrodynamicshttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Irrotationalhttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Electrostatic_potentialhttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Work_(physics)http://en.wikipedia.org/wiki/Classical_electromagnetismhttp://en.wikipedia.org/wiki/Scalar_(physics)http://en.wikipedia.org/wiki/Electric_potential_energyhttp://en.wikipedia.org/wiki/Joulehttp://en.wikipedia.org/wiki/Electric_chargehttp://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Jouleshttp://en.wikipedia.org/wiki/Coulombhttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Scalar_potentialhttp://en.wikipedia.org/wiki/Electrodynamics


15/22

in eit&er t&e same or t&e opposite direction of t&e electric field. ,f t&e c&ar"ed

ob9ect &as a positi)e c&ar"e t&e force and acceleration will be in t&e direction of

t&e field. $&is force &as t&e same direction as t&e electric field )ector and its

ma"nitude is "i)en b# t&e sie of t&e c&ar"e multiplied wit& t&e ma"nitude of

t&e electric field.Classical mec&anicse!plores t&e concepts suc&

asforceener"# potentialetc. $&e electric potential *or potential+ at a point in

an electric field is defined as t&e wor/ done in mo)in" a unit positi)e c&ar"e

from infinit# to t&at point.

$&e electric potential and t&ema"netic )ector potentialto"et&er form afour

)ector so t&at t&e two /inds of potential are mi!ed underorent

transformations.

#n electrostatics

$&e electric potential at a pointrin a static electric fieldEis "i)en b# t&eline

inte"ral

w&ere'is an arbitrar# pat& connectin" t&e point wit& ero potential tor. U&en

t&ecurlJEis ero t&e line inte"ral abo)e does not depend on t&e specific

pat&'c&osen but onl# on its endpoints. ,n t&is case t&e electric field

isconser)ati)eand determined b# t&e"radientof t&e potential;

$&en b#Gauss's law t&e potential satisfiesPoisson's equation;

w&ereis t&e totalc&ar"e densit#*includin"bound c&ar"e+ and denotes

t&edi)er"ence.
http://en.wikipedia.org/wiki/Electric_field_vectorhttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Force_(physics)http://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Potentialhttp://en.wikipedia.org/wiki/Magnetic_vector_potentialhttp://en.wikipedia.org/wiki/Magnetic_vector_potentialhttp://en.wikipedia.org/wiki/Four_vectorhttp://en.wikipedia.org/wiki/Four_vectorhttp://en.wikipedia.org/wiki/Lorentz_transformationhttp://en.wikipedia.org/wiki/Lorentz_transformationhttp://en.wikipedia.org/wiki/Line_integralhttp://en.wikipedia.org/wiki/Line_integralhttp://en.wikipedia.org/wiki/Curl_(mathematics)http://en.wikipedia.org/wiki/Conservative_vector_fieldhttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Gauss's_lawhttp://en.wikipedia.org/wiki/Poisson's_equationhttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Bound_chargehttp://en.wikipedia.org/wiki/Divergencehttp://en.wikipedia.org/wiki/Electric_field_vectorhttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Force_(physics)http://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Potentialhttp://en.wikipedia.org/wiki/Magnetic_vector_potentialhttp://en.wikipedia.org/wiki/Four_vectorhttp://en.wikipedia.org/wiki/Four_vectorhttp://en.wikipedia.org/wiki/Lorentz_transformationhttp://en.wikipedia.org/wiki/Lorentz_transformationhttp://en.wikipedia.org/wiki/Line_integralhttp://en.wikipedia.org/wiki/Line_integralhttp://en.wikipedia.org/wiki/Curl_(mathematics)http://en.wikipedia.org/wiki/Conservative_vector_fieldhttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Gauss's_lawhttp://en.wikipedia.org/wiki/Poisson's_equationhttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Bound_chargehttp://en.wikipedia.org/wiki/Divergence


16/22

$&e concept of electric potential is closel# lin/ed wit&potential ener"#. :test

c&ar"eq&as anelectric potential ener"#(E"i)en b#

$&e potential ener"# and &ence also t&e electric potential is onl# defined up to

an additi)e constant; one must arbitraril# c&oose a position w&ere t&e potential

ener"# and t&e electric potential are ero.

$&ese equations cannot be used if t&e curlJEV 8 i.e. in t&e case of

anonconser)ati)e electric field*caused b# a c&an"in"ma"netic fieldK

seea!well's equations+. $&e "eneraliation of electric potential to t&is case is

described below.

Electric potential due to a point charge

$&e electric potential created b# a point c&ar"eQ at a distancerfrom t&e

c&ar"e *relati)e to t&e potential at infinit#+ can be s&own to be

w&ere8is t&eelectric constant*permitti)it# of free space+. $&is is /nown as t&e

Coulomb Potential.

$&e electric potential due to a s#stem of point c&ar"es is equal to t&e sum of t&e

point c&ar"es' indi)idual potentials. $&is fact simplifies calculations

si"nificantl# since addition of potential *scalar+ fields is muc& easier t&an

addition of t&e electric *)ector+ fields.

$&e equation "i)en abo)e for t&e electric potential *and all t&e equations used

&ere+ are in t&e forms required b#-, units. ,n some ot&er *less common+

s#stems of units suc& asCG-(Gaussian man# of t&ese equations would be

altered.
http://en.wikipedia.org/wiki/Potential_energyhttp://en.wikipedia.org/wiki/Test_chargehttp://en.wikipedia.org/wiki/Test_chargehttp://en.wikipedia.org/wiki/Electric_potential_energyhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Maxwell's_equationshttp://en.wikipedia.org/wiki/Electric_constanthttp://en.wikipedia.org/wiki/SI_unitshttp://en.wikipedia.org/wiki/SI_unitshttp://en.wikipedia.org/wiki/Gaussian_unitshttp://en.wikipedia.org/wiki/Potential_energyhttp://en.wikipedia.org/wiki/Test_chargehttp://en.wikipedia.org/wiki/Test_chargehttp://en.wikipedia.org/wiki/Electric_potential_energyhttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Maxwell's_equationshttp://en.wikipedia.org/wiki/Electric_constanthttp://en.wikipedia.org/wiki/SI_unitshttp://en.wikipedia.org/wiki/Gaussian_units


17/22

=ote t&at t&is definition ofVdepends on t&e"au"e c&oicefor t&e )ector

potential$*t&e"radientof an# scalar field can be added to$wit&out

c&an"in"(+. One c&oice is t&eCoulomb "au"e in w&ic& we c&oose$ 8.

,n t&is case we obtain

w&ereis t&ec&ar"e densit# 9ust as for electrostatics. :not&er common c&oice

is t&eoren "au"e in w&ic& we c&oose$to satisf#

)nits$&e-,unit of electric potential is t&e)olt*in &onor of:lessandro Nolta+ w&ic&

is w electric potential is also /nown as)olta"e. Older units are rarel# used

nowada#s. Nariants of t&ecentimeter "ram second s#stem of unitsincluded a

number of different units for electric potential includin" t&eab)oltand

t&estat)olt.

Electrostatic energyEner"# due to a c&ar"e distribution is obtained b# a triple

inte"ral; in w&ic& N represents t&e )olume of c&ar"e

distribution.

Electrostatic generators

$&e presence ofsurface c&ar"eimbalance means t&at t&e ob9ects will e!&ibit

attracti)e or repulsi)e forces. $&is surface c&ar"e imbalance w&ic& #ields static

electricit# can be "enerated b# touc&in" two differin" surfaces to"et&er and

t&en separatin" t&em due to t&e p&enomena ofcontact electrificationand
http://en.wikipedia.org/wiki/Gauge_fixinghttp://en.wikipedia.org/wiki/Gauge_fixinghttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Coulomb_gaugehttp://en.wikipedia.org/wiki/Coulomb_gaugehttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Lorenz_gaugehttp://en.wikipedia.org/wiki/SIhttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Alessandro_Voltahttp://en.wikipedia.org/wiki/Alessandro_Voltahttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Centimeter_gram_second_system_of_unitshttp://en.wikipedia.org/wiki/Conversion_of_units#Electromotive_forcehttp://en.wikipedia.org/wiki/Conversion_of_units#Electromotive_forcehttp://en.wikipedia.org/wiki/Statvolthttp://en.wikipedia.org/wiki/Surface_chargehttp://en.wikipedia.org/wiki/Contact_electrificationhttp://en.wikipedia.org/wiki/Gauge_fixinghttp://en.wikipedia.org/wiki/Gradienthttp://en.wikipedia.org/wiki/Coulomb_gaugehttp://en.wikipedia.org/wiki/Charge_densityhttp://en.wikipedia.org/wiki/Lorenz_gaugehttp://en.wikipedia.org/wiki/SIhttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Alessandro_Voltahttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Centimeter_gram_second_system_of_unitshttp://en.wikipedia.org/wiki/Conversion_of_units#Electromotive_forcehttp://en.wikipedia.org/wiki/Statvolthttp://en.wikipedia.org/wiki/Surface_chargehttp://en.wikipedia.org/wiki/Contact_electrification


18/22

t&etriboelectric effect. Mubbin" two nonconducti)e ob9ects "enerates a "reat

amount of static electricit#. $&is is not 9ust t&e result of frictionK two

nonconducti)e surfaces can become c&ar"ed b# 9ust bein" placed one on top of

t&e ot&er. -ince most surfaces &a)e a rou"& te!ture it ta/es lon"er to ac&ie)e

c&ar"in" t&rou"& contact t&an t&rou"& rubbin". Mubbin" ob9ects to"et&er

increases amount of ad&esi)e contact between t&e two surfaces.

Wsuall#insulators e.". substances t&at do not conduct electricit# are "ood at

bot& "eneratin" and &oldin" a surface c&ar"e. -ome e!amples of t&ese

substances arerubberplastic"lass andpit&.Conducti)eob9ects onl# rarel#

"enerate c&ar"e imbalance e!cept for e!ample w&en a metal surface is

impacted b# solid or liquid nonconductors. $&e c&ar"e t&at is transferred durin"

contact electrification is stored on t&e surface of eac& ob9ect.-tatic electric

"enerators de)ices w&ic& produce )er# &i"& )olta"e at )er# low current and

used for classroom psics demonstrations rel# on t&is effect.

=ote t&at t&e presence ofelectric currentdoes not detract from t&e electrostatic

forces nor from t&e spar/in" from t&ecorona disc&ar"e or ot&er p&enomena.Lot& p&enomena can e!ist simultaneousl# in t&e same s#stem.

.

Charge neutrali*ation

=atural electrostatic p&enomena are most familiar as an occasional anno#ance

in seasons of low &umidit# but can be destructi)e and &armful in some

situations *e.". electronics manufacturin"+. U&en wor/in" in direct contact wit&

inte"rated circuit electronics *especiall# delicateO-FE$s+ or in t&e presence

of flammable "as care must be ta/en to a)oid accumulatin" and suddenl#

disc&ar"in" a static c&ar"e *seeelectrostatic disc&ar"e+.
http://en.wikipedia.org/wiki/Triboelectric_effecthttp://en.wikipedia.org/wiki/Insulatorshttp://en.wikipedia.org/wiki/Rubberhttp://en.wikipedia.org/wiki/Plastichttp://en.wikipedia.org/wiki/Glasshttp://en.wikipedia.org/wiki/Pithhttp://en.wikipedia.org/wiki/Conductor_(material)http://en.wikipedia.org/wiki/Electrostatic_generatorhttp://en.wikipedia.org/wiki/Electrostatic_generatorhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Corona_dischargehttp://en.wikipedia.org/wiki/MOSFEThttp://en.wikipedia.org/wiki/Electrostatic_dischargehttp://en.wikipedia.org/wiki/Triboelectric_effecthttp://en.wikipedia.org/wiki/Insulatorshttp://en.wikipedia.org/wiki/Rubberhttp://en.wikipedia.org/wiki/Plastichttp://en.wikipedia.org/wiki/Glasshttp://en.wikipedia.org/wiki/Pithhttp://en.wikipedia.org/wiki/Conductor_(material)http://en.wikipedia.org/wiki/Electrostatic_generatorhttp://en.wikipedia.org/wiki/Electrostatic_generatorhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Corona_dischargehttp://en.wikipedia.org/wiki/MOSFEThttp://en.wikipedia.org/wiki/Electrostatic_discharge


19/22

Charge induction

C&ar"e induction occurs w&en a ne"ati)el# c&ar"ed ob9ect repels electrons from

t&e surface of a second ob9ect. $&is creates a re"ion in t&e second ob9ect t&at is

more positi)el# c&ar"ed. :n attracti)e force is t&en e!erted between t&e ob9ects.

For e!ample w&en a balloon is rubbed t&e balloon will stic/ to t&e wall as an

attracti)e force is e!erted b# two oppositel# c&ar"ed surfaces *t&e surface of t&e

wall "ains an electric c&ar"e due to c&ar"e induction as t&e free electrons at t&e

surface of t&e wall are repelled b# t&e ne"ati)e balloon creatin" a positi)e wall

surface w&ic& is subsequentl# attracted to t&e surface of t&e balloon+. Xou can

e!plore t&e effect wit& a simulation of t&eballoon and static electricit#.c&ar"e

induction mean w&en a c&ar"ed bod# is brou"&t nearer to anot&er unc&ar"ed

bod#*metallic or non conduction+t&en front face of t&e unc&ar"ed bod# is seen

to be oppositel# c&ar"e t&is s&ows attraction and t&e p&enomenon is called

electrostatics. =O$E($wo similar c&ar"e bod# can attract eac& ot&er w&en one

bod# &a)e lar"e amount of c&ar"e and anot&er &a)e small amount of c&ar"e b#

t&e induction.its also &apeen in insulator.

Electrostatic induction

Electrostatic inductionis a redistribution of electrical c&ar"ein an ob9ect

caused b# t&e influence of nearb# c&ar"es. ,nduction was disco)ered b# Lritis&

scientist Yo&n Cantonin 1>53 and -wedis& professor Yo&an Carl Uilc/ein

1>%2. Electrostatic "enerators suc& as t&e Uims&urst mac&ine t&e Nan de

Graaff "eneratorand t&e electrop&orus use t&is principle. ,nduction is also

responsible for t&e attraction of li"&t nonconducti)e ob9ects suc& as balloons

paper or st#rofoam scraps to static electric c&ar"es. Electrostatic induction

s&ould not be confused wit& electroma"netic induction.
http://phet.colorado.edu/new/simulations/sims.php?sim=Balloons_and_Static_Electricityhttp://en.wikipedia.org/wiki/Electrical_chargehttp://en.wikipedia.org/wiki/John_Cantonhttp://en.wikipedia.org/wiki/Johan_Carl_Wilckehttp://en.wikipedia.org/wiki/Electrostatic_generatorhttp://en.wikipedia.org/wiki/Wimshurst_machinehttp://en.wikipedia.org/wiki/Van_de_Graaff_generatorhttp://en.wikipedia.org/wiki/Van_de_Graaff_generatorhttp://en.wikipedia.org/wiki/Electrophorushttp://en.wikipedia.org/wiki/Electromagnetic_inductionhttp://phet.colorado.edu/new/simulations/sims.php?sim=Balloons_and_Static_Electricityhttp://en.wikipedia.org/wiki/Electrical_chargehttp://en.wikipedia.org/wiki/John_Cantonhttp://en.wikipedia.org/wiki/Johan_Carl_Wilckehttp://en.wikipedia.org/wiki/Electrostatic_generatorhttp://en.wikipedia.org/wiki/Wimshurst_machinehttp://en.wikipedia.org/wiki/Van_de_Graaff_generatorhttp://en.wikipedia.org/wiki/Van_de_Graaff_generatorhttp://en.wikipedia.org/wiki/Electrophorushttp://en.wikipedia.org/wiki/Electromagnetic_induction


20/22

Eplanation

Demonstration of induction, in 1870s. The positive terminal of an electrostatic

machineis placed near the brass cylinder, causing the left side to acuire a

positive charge and the right to acuire a negative charge. The small pith ball

electroscopeshanging from the bottom sho! that the charge is concentrated at

the ends.

Charging an ob+ect by induction

"old#leaf electroscope, sho!ing induction, before the terminal is grounded.

owe)er t&e induction effect can also be used to put a net c&ar"e on an ob9ect.

,f w&ile it is close to t&e positi)e c&ar"e t&e abo)e ob9ect is momentaril#

connected t&rou"& a conducti)epat& to electrical "round w&ic& is a lar"e

reser)oir of bot& positi)e and ne"ati)e c&ar"es some of t&e ne"ati)e c&ar"es in
http://en.wikipedia.org/wiki/Electrostatic_machinehttp://en.wikipedia.org/wiki/Electrostatic_machinehttp://en.wikipedia.org/wiki/Pith_ball_electroscopehttp://en.wikipedia.org/wiki/Pith_ball_electroscopehttp://en.wikipedia.org/wiki/Electrical_conductorhttp://en.wikipedia.org/wiki/Ground_(electricity)http://en.wikipedia.org/wiki/File:Electroscope_showing_induction.pnghttp://en.wikipedia.org/wiki/File:Electrostatic_induction_experiment.pnghttp://en.wikipedia.org/wiki/Electrostatic_machinehttp://en.wikipedia.org/wiki/Electrostatic_machinehttp://en.wikipedia.org/wiki/Pith_ball_electroscopehttp://en.wikipedia.org/wiki/Pith_ball_electroscopehttp://en.wikipedia.org/wiki/Electrical_conductorhttp://en.wikipedia.org/wiki/Ground_(electricity)


21/22

t&e "round will flow into t&e ob9ect under t&e attraction of t&e nearb# positi)e

c&ar"e. U&en t&e contact wit& "round is bro/en t&e ob9ect is left wit& a net

ne"ati)e c&ar"e.

$&is met&od can be demonstrated usin" a "old(leaf electroscope w&ic& is an

instrument for detectin" electric c&ar"e. $&e electroscope is first disc&ar"ed and

a c&ar"ed ob9ect is t&en brou"&t close to t&e instrument's top terminal. ,nduction

causes a redistribution of t&e c&ar"es inside t&e electroscope's metal rod so t&at

t&e top terminal "ains a net c&ar"e of opposite polarit# to t&at of t&e ob9ect

w&ile t&e "old lea)es "ain a c&ar"e of t&e same polarit#. -ince bot& lea)es &a)e

t&e same c&ar"e t&e# repel eac& ot&er and spread apart. $&e electroscope &as

not acquired a net c&ar"e; t&e c&ar"e wit&in it &as merel# been redistributed so

if t&e c&ar"e were to be mo)ed awa# from t&e electroscope t&e lea)es will come

to"et&er a"ain.

The electrostatic field inside a conductive ob+ect is *ero

$urface charges induced in metal ob%ects by a nearby charge. The electrostatic

&eld(lines with arrows)of a nearby positive charge (+)causes the mobile

charges in metal ob%ects to separate. 'egative charges (blue)are attracted and

move to the surface of the ob%ect facing the e(ternal charge. )ositive
http://en.wikipedia.org/wiki/Gold-leaf_electroscopehttp://en.wikipedia.org/wiki/Electroscopehttp://en.wikipedia.org/wiki/Electroscopehttp://en.wikipedia.org/wiki/Electrostatic_fieldhttp://en.wikipedia.org/wiki/Electrostatic_fieldhttp://en.wikipedia.org/wiki/File:Electrostatic_induction.svghttp://en.wikipedia.org/wiki/Gold-leaf_electroscopehttp://en.wikipedia.org/wiki/Electroscopehttp://en.wikipedia.org/wiki/Electrostatic_fieldhttp://en.wikipedia.org/wiki/Electrostatic_field


22/22

charges (red)are repelled and move to the surface facing a!ay. These induced

surface charges create an opposing electric &eld that e(actly cancels the &eld of

the e(ternal charge throughout the interior of the metal. Therefore electrostatic

induction ensures that the electric &eld every!here inside a conductive ob%ect is

*ero.

: remainin" question is &ow lar"e t&e induced c&ar"es are. $&e mo)ement of

c&ar"e is caused b# t&e force e!erted b# t&eelectric fieldof t&e e!ternal c&ar"ed

ob9ect. :s t&e c&ar"es in t&e metal ob9ect continue to separate t&e resultin"

positi)e and ne"ati)e re"ions create t&eir own electric field w&ic& opposes t&e

field of t&e e!ternal c&ar"e. $&is process continues until )er# quic/l# *wit&in a

fraction of a second+ an equilibriumis reac&ed in w&ic& t&e induced c&ar"es are

e!actl# t&e ri"&t sie to cancel t&e e!ternal electric field t&rou"&out t&e interior

of t&e metal ob9ect. $&en t&e remainin" mobile c&ar"es *electrons+ in t&e

interior of t&e metal no lon"er feel a force and t&e net motion of t&e c&ar"es

stops.
http://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Equilibrium_statehttp://en.wikipedia.org/wiki/Electric_fieldhttp://en.wikipedia.org/wiki/Equilibrium_state

electrostatics temp

Documents