ap ch. 20 notes
TRANSCRIPT
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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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&le '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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• &le '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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&le '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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&le '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