崩溃电场介电常数介电材料

Thelifesavingjoltofadefibrillatorrequiresalargeamountofenergydeliveredinashorttime.除纖顫器救命的電擊需要在短時間內送出大批能量。Wheredoesthatenergycomefrom?這些能量從何而來？Capacitor電容器23.1.ElectrostaticEnergy 靜電能ElectrostaticEnergy=workdonetoassemblethechargeconfigurationofasystem.靜電能

=裝組系統的電荷配置所需做的功。Reference參考(0energy能):whenallcomponentchargesarewidelyseparated.當所有的組分電荷都相隔甚遠時。Bringingq1inplacetakesnowork.把q1歸位不需做功Bringinginq2takes把q2歸位需功Bringinginq3takes把q3歸位需功Totalelectrostaticenergy總靜電能23.2.Capacitors 電容器Capacitor:pairofconductorscarryingequalbutoppositecharges.電容器：帶著等量異性電荷的一對導體。Usage:storeelectricalenergy用途：存儲電能Parallel-PlateCapacitor 平行板電容器:2conductingplatesofareaAseparatedbyasmalldistanced.兩塊相隔短距離d，面積為A的導體板。Platesareinitiallyneutral. 開始時兩塊板都是中性。They’rechargedbyconnectingtoabattery. 接上電瓶後起電。Chargetransferplatesareequalbutoppositelycharged.電荷轉移

兩塊板的電荷量等而性異。LargeA,smalld

E0outside.

大A，小d

器外的E0。Farfromtheedges離邊遠處Capacitance 電容量Parallel-platecapacitor:平行板電容器：

C=Q/V=capacitance電容量Parallel-platecapacitor平行板電容器SeeProbs參閱習題41&42Practicalcapacitor~F(106F)orpF(1012F)實用電容器Charging/Discharging充/放電EnergyStoredinCapacitors 存在電容器內的電能WhenpotentialdifferencebetweencapacitorplatesisV, 電容器兩板之間的電位差為V時，workrequiredtomovechargedQfromto+plateis 把電荷dQ從

移至+板需作功Workrequiredtochargethecapacitorfrom0toVis把電容器從0充電至V需作功=U=energystoredincapacitor

存在電容器內的電能Note注意:Ina“charged”capacitor,Qisthechargeonthe+plate.在一個”帶電”的電容器內，Q是+板上的電荷。Thetotalchargeofthecapacitorisalwayszero.電容器的總電荷永遠為零。E

dr<0Example23.1.Parallel-PlateCapacitor 平行板電容器AcapacitorconsistsoftwocircularmetalplatesofradiusR=12cm,separatedbyd=5.0mm.一個電容器由兩塊圓形金屬板組成；板的半徑為R=12cm，相距d=5.0mm。Find求

Itscapacitance 其電容量，thechargeontheplates,and 板上電荷，和thestoredenergywhenthecapacitorisconnectedtoa12-Vbattery.電容器在接上一個12-V電瓶後所存的能量。(a)(b)(c)23.3.UsingCapacitors 使用電容器Computermemories:billionsof25fFcapacitors.電腦記憶體：數十億個25fF電容器。Rectifiers整流器： mF Fuel-cells燃料電池: 102F220-mFelectrolyticcapacitor電解電容器1F43pFto2.2mFPracticalCapacitors 實用電容器Inexpensivecapacitors 廉價電容器:Thinplasticsandwichedbetweenaluminumfoils&rolledintocylinder.薄塑料夾在兩鋁片間再捲成圓筒。Electrolyticcapacitors電解電容器(largecapacitance 大電容量):Insulatinglayerdevelopedbyelectrolysis. 絕緣層以電解生成。CapacitorsinICcircuitsIC電路中的電容器(smallcapacitance小電容量):Alternatingconductive&insulatinglayers. 導體層和絕緣層交替。Dielectrics 介電體Dielectrics:insulatorscontainingmoleculardipolesbutnofreecharges.介電體：含有分子雙極但沒有自由電荷的絕緣體DielectriclayerlowersVbetweencapacitorplatesbyfactor1/(>1).電容器兩板間的介電質層把V降低1/(>1)倍。=dielectricconstant介電常數MoleculardipolesalignedbyE0.分子雙極依E0排向DipolefieldsopposeE0. 雙極場與E0反向。NetfieldreducedtoE=E0/

. 淨場減至

E=E0/

。HenceV=V0/

. 故V=V0/

。Qisunchanged,soC=

C0

. Q

不變，所以C=

C0

。

:2~10mostlyWorkingvoltageV=Maxsafepotential<Ebkdd工作電壓V=最大安全電位<Ebkdd崩潰電場介電常數介電材料表23.1常見介電體的性質氧化鋁Example23.2.WhichCapacitor? 那個電容器？A100-Fcapacitorhasaworkingvoltageof20V, 一個100-F電容器的運作電壓為20V，whilea1.0-Fcapacitorisratedat300V. 另一個1.0-F電容器可承受300V。Whichcanstoremorecharge?Moreenergy? 那一個可以儲存較多電荷？較多能量？GOTIT?23.1.Youneedtoreplaceacapacitorwithonethatcanstoremoreenergy.你需要把一個電容器換成一個存能較多的。Whichwillgiveyougreaterenergyincrease:下面那一個會給你較多的能量：acapacitorwithtwicethecapacitanceandsameworkingvoltageastheoldone,一個電容量是舊的二倍，運作電壓卻和它一樣的電容器，or或acapacitorwiththesamecapacitanceandtwicetheworkingvoltage?一個電容量和舊的一樣，運作電壓卻是它二倍的電容器？ConnectingCapacitors 連接電容器Twowaystoconnect2electroniccomponents:parallel&series兩個方法連接兩個電子元件：並聯和串聯Parallel:SameVforbothcomponents並聯：兩元件的V一樣

Series:SameI(Q)forbothcomponents串聯：兩元件的I(Q)

一樣

ConceptualExample23.1.Parallel&SeriesCapacitors並聯與串聯電容Usingparallel-platecapacitors,explainwhycapacitanceshouldincreasewithcapcitorsinparallelandecreasewithcapacitorsinseries.用平板電容器來闡述為何並聯會增大電容量，串聯則減少電容量。Whathappenstotheworkingvoltageineachcase? 工作電壓又會怎樣？Parallel-platecapacitor:平板電容器:inparallel並聯A=A1+A

2

Cincreases增大inseries串聯d=d1+d

2

Cdecreases減少Vworking

=min(Vw1,Vw2

)Vworking

<Vw1+Vw2MakingtheConnection 連起來You’vegottwo10-Fcapacitorsratedat15V. 你有兩個15V級的10-F電容量。Whatarethecapacitances&workingvoltagesoftheirparallel&seriescombinations?它們並聯和串聯後的電容量和工作電壓為何?Parallel:並聯:Series:串聯:

GOTIT?23.2.Youhave2identicalcapacitorswithcapacitanceC.你有兩個一樣的電容器，電容量都是C。Howwouldyouconnectthemtogetequivalentcapacitances你會如何把它們連接來達到以下的電容量？2C,and和½C?Whichcombinationwouldhavethehigherworkingvoltage?那一個組合有較高的運作電壓？parallel並聯series串聯Example23.2.ConnectingCapacitors 連接電容器FindtheequivalentcapacitanceofthecombinationsshownintheFigure.求圖中所示組合的相當電容量。IfthemaximumvoltagetobeappliedbetweenpointsAandBis100V,如果加到A和B之間的最高電壓是100V，whatshouldbetheworkingvoltageofC1? C1的運作電壓為何？(min.workingvoltage)最小運作電壓BurstsofPower 爆發性電力

SanFrancisco’sBARTtrain三藩市的灣區捷運:KEofdecelerationstoredasEEinultracapacitor.減速時的KE以EE存於超級電容器中。StoredEEisusedtoacceleratetrain. 儲存的EE再用來加速。Capacitorsdeliverhigherenergymuchmorequicklythanbatteries.電容器送出的能量可以比電瓶的更大和更快。Flashlight閃光燈:Batterychargescapacitor,whichthendischargestogiveflash.電容器經電池充電後放電以產生閃光。Otherexamples其他例子:Defibrillator,controllednuclearfusion,amusementparkrides,hybridcars,…除纖顫器，受控的核子融合，遊樂場的設施，混合動力汽車，…23.4.EnergyintheElectricField 電場中的能ChargingacapacitorrearrangeschargesenergystoredinE

電容器充電時把電荷重組

能量存到E中Energydensity=energyperunitvolume能量密度

=單位體積內的能量Parallel-platecapacitor:平行板電容器：Energydensity:能量密度：isuniversal是通用的Example23.4.AThunderstorm 雷雨Typicalelectricfieldsinthunderstormsaveragearound105V/m.雷雨中的電場一般平均有105V/m。Consideracylindricalthundercloudwithheight10kmanddiameter20km,茲有一圓筒型雷雨雲塊，其高為10km，其直徑為20km，andassumeauniformelectricfieldof1105V/m.

假定其均勻電場為1105V/m。Findtheelectricenergycontainedinthisstorm.求此風暴所藏電能。~1400gallonsofgasoline.

加侖汽油Example23.5.AShrinkingSphere 一個縮小的球AsphereofradiusR1carrieschargeQdistributeduniformlyoveritssurface.一半徑為R1的球帶有一均勻分佈於其表面的電荷Q。Howmuch