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Ch. 20 ElectricPotential and

Electric Potential

Energy

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Electric Potential Energy

• Electrical potential energy is theenergy contained in a confgurationo charges. Like all potentialenergies, when it goes up theconfguration is less stable; when itgoes down, the confguration is ore

stable.•  !he unit is the "oule.

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E#uation

•  ∆$ % & ' % #0Ed

• #0 ( test charge

•

E ( Electric feld• d & distance

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increaseswhen charges are brought into

lessfavorable congurations

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Electrical potential energydecreases when charges are

brought into more favorablecongurations.

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Work must be done on thecharge to increase the electric

potential energy

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• )or a positive test charge to be o*edupward a distance d, the electric orcedoes negative work.

•  !he electric potential energy hasincreased and $ is positive +$2 $-

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• / a negative charge is o*ed upward adistance d, the electric orce doespositive work.

•  !he change in the electric potentialenergy U is negative (U2 < U1)

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Electric Potential +

Electric potential is hard tounderstand, but easy to easure.

• 'e coonly call it 1*oltage, andits unit is the olt.

• - % - "3C

•

Electric potential is easily related toboth the electric potential energy,and to the electric feld.

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•  !he change in potential energy is directlyrelated to the change in *oltage.

∆$ % #∆∆ % ∆$3#

•

 ∆$4 change in electrical potential energy+"

•  #4 charge o*ed +C

•  ∆4 potential di5erence +• 6ll charges will spontaneously go to lower

potential energies i they are allowed to

o*e.

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• 7ince all charges try to decrease U!and ∆$E % #∆, this eans that

spontaneous o*eent o charges resultin negative ∆$.

•  " # U $ %

• Positi*e charges like to 8EC9E67E theirpotential +∆ : 0

• egati*e charges like to /C9E67E theirpotential. +∆ 0

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&ample 'roblem *.+ ,- charge ismoved through a potential dierenceof /0+ ". What is its potential energ

change

El i l P i l i

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Electrical Potential in$nior Electric )ields

 !he electric potential is related in asiple way to a unior electric feld.

 " # 3d•  ∆4 change in electrical potential +

• E4 Constant electric feld strength+3C or 3

• d4 distance o*ed +

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• &ample 'roblem n electric eld isparallel to the 43a4is. What is itsmagnitude and direction if the

potential dierence between 4 #1.+m and 4 # 2.5 m is found tobe 67++ "

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& l ' bl 8f t i

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&ample 'roblem 8f a proton isaccelerated through a potentialdierence of 2.+++ "! what is its

change in potential energ 

:ow fast will this proton be moving ifit started at rest

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& l ' bl t t t i

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&ample 'roblem proton at rest isreleased in a uniform electric eld.What potential dierence must it

move through in order to ac%uire aspeed of +.2+ c

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El t i P t ti l E

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Electric Potential Energy or7pherical Charges

• Electric potential energy is a scalar, likeall ors o energy.

$ % k#-#23r•  $4 electrical potential energy +"

•  k4 -0=  2 3 C2

•  #-, #2 4 charges +C

•  r4 distance between centers +

!his orula onl works for spherical

charges or point charges.

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6bsolute Electric Potential+spherical

• )or a spherical or point charge, theelectric potential can be calculated bythe ollowing

)orula4 % k#3r•  4 potential +

•  k4

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20 @ E#uipotential 7uraces and the

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20&@ E#uipotential 7uraces and theElectric )ield

)or two point charges4

E i t ti l 7 d

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E#uipotential 7uraces andthe Electric )ield

6n ideal conductor is an e#uipotential surace.!hereore, i two conductors are at the saepotential, the one that is ore cur*ed will ha*e alarger electric feld around it. !his is also true ordi5erent parts o the sae conductor.

E i t ti l 7 d

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E#uipotential 7uraces andthe Electric )ield

!here are electric felds inside the huanbody; the body is not a perect conductor,so there are also potential di5erences.

6nelectrocardiograph plots the heartAs

electrical acti*ity.

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Capacitor

• aed or the capacity to storeelectric charge and energy.

• 6 capacitor is two conducting platesseparated by a fnite distance4

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 !he capacitance relates the

charge to the potentialdi5erence4

7aple Proble4 6 0 B ) capacitor is

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7aple Proble4 6 0.B ) capacitor ischarged to a *oltage o -D *olts. 'hat isthe agnitude o the charge on each

plate o the capacitor

7aple Proble4 6 0.B µ) capacitor is charged

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7aple Proble4 6 0.B µ) capacitor is chargedto a *oltage o -D *olts. 'hat is the agnitudeo the charge on each plate o the capacitor

% -D , C % 0.B µ) % 0.B ?-0&D )

F %C % F3 or F % C

F % +0.B ? -0&D+-DF % -.2 ? -0& C

6 siple type o capacitor is the parallel&

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6 siple type o capacitor is the parallelplate capacitor. /t consists o two plateso area  A separated by a distance d .

Gy calculating theelectric feld created

by the charges ±Q,we fnd that thecapacitance o a

parallel&platecapacitor is4

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Capacitor Heoetry !he capacitance o a

capacitor dependson IJ' you ake it.

2

2

12o

o

1085.8

constantty permittivivacuum

ality proportionof constant

 plates beteweendistanced

 plateof area

d

1

 NmC  x

d 

 A

C 

 A

C  AC 

o

−=

=

=

=

=

ε 

ε 

ε 

α 

α α 

d

 AC    o

ε 

=

• 7aple Proble4 'hat is

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• 7aple Proble4 'hat isthe 69E6 o a - ) capacitor

that has a plate separationo -

C % - ), d % - % 0.00-, εο %

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=

=

=

=

−

Sides

 A

 A x

 D

 AC  o

001.01085.81   12

ε 

1.1* 4 1+ m2

1+/27 m

8s this a practical capacitor

JK ( Iow can you build this th

 !he answer lies in9E8$C/H the 69E6.

Gut you ust ha*e aC6P6C/!6CE o - ).:ow can ou keep

the capacitance at1 = and reduce therea at the sametime

dd a >8?-;@8 6 dielectric is an insulator; when placed

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6 dielectric is an insulator; when placedbetween the plates o a capacitor it gi*es alower potential di5erence with the sae

charge, due to the polariation o theaterial. !his increases the capacitance.

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8ielectric9eeber, the dielectric is an insulating aterial placed

between the conductors to help store the charge. /n thepre*ious e?aple we assued there was J dielectricand thus a *acuu between the plates.

Dielectric=

=

k d 

 Ak C  oε 

6ll insulating aterials

ha*e a dielectricconstant associatedwith it. Iere now youcan reduce the 69E6

and use a L69HE

7aple Proble4 6 parallel plate capacitor is

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p p p pconstructed with plate o an area o 0.02< 2 and a separation o 0. . )ind the

agnitude o the charge o this capacitor whenthe potential di5erence between the plate is20.- .

6 % 0.02< 2 d %0. % 0.000, %20.-

F % F % C

  C % εο 63d C%+

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!he polariation o the dielectric results ina lower electric feld within it; the new feldis gi*en by di*iding the original feld by the

dielectric constant κ4

!hereore, the capacitancebecoes4

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 !he dielectricconstant is a

property othe aterial;

here are soee?aples4

$sing MJ9E than -

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$sing MJ9E than -capacitorLetAs say you decide that

- capacitor will not beenough to build whatyou need to build. Nouay need to use orethan -. !here are 2basic ways toasseble thetogether

• 7eries ( Jne ateranother

• Parallel ( between aset o Ounctions andparallel to each other.

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Capacitors in 7eriesCapacitors in series each charge each other by /8$C!/J.

7o they each ha*e the 76ME charge. !he electricpotential on the other hand is di*ided up aongst the./n other words, the su o the indi*idual *oltages wille#ual the total *oltage o the battery or power source.

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Capacitors in Parallel/n a parallel confguration, the voltage is the

same because 6LL !I9EE capacitors touchGJ!I ends o the battery. 6s a result, theysplit up the charge aongst the.

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Capacitors 17!J9E energy6nytie you ha*e a situation where energy is 17!J9E8 it is called

PJ!E!/6L. /n this case we ha*e capacitor potential energy, $c

7uppose we plot a *s. Fgraph. / we wanted to fnd the69E6 we would M$L!/PLN the 2*ariables according to thee#uation or 6rea.

6 % bh

'hen we do this we get 6rea% F

LetAs do a unit checkK

oltage % "oules3CoulobCharge % Coulobs6rea %

B@CD 

Potential Energy o a

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Potential Energy o aCapacitor7ince the 69E6 under the line is a

triangle, the EE9HN+area%-32F

C 

QQ

C 

QU 

CV VC V U 

V 

QC VQU 

C 

C 

C 

2)(

21

21)(21

21

2

2

→=

→=

==

 !his energy or area isreerred as the potentialenerg stored inside acapacitor.

ote4 !he slope o the lineis the in*erse o thecapacitance.

ost coon or

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G. )ind the energy stored in the

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G. )ind the energy stored in thecharged up defbrillator.

$ % 7ince you now know F, C, Q . Nouay use any o the e#uations to

fnd $.$ % R C2  $ % R F $ % F23+2C

$ % R +0.=2+22@0

$ % @= "

•  !he energy stored in a capacitor can be put

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to a nuber o uses4 a caera Sash; acardiac defbrillator; and others. /n addition,

capacitors or an essential part o ostelectrical de*ices used today.

• / we di*ide the stored energy by the

*olue o the capacitor, we fnd the energyper unit *olue; this result is *alid or anyelectric feld4

/ the electric feld in a dielectric becoes

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too large, it can tear the electrons o5 theatos, thereby enabling the aterial to

conduct.

 !his is calleddielectric

breakdown;the feld atwhich thishappens iscalled thedielectric