Class 02 - Jan 17 (Ch. 22) - w notes PDF

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Introductory Info + Important Dates  Syllabus:AvailableonBlackboardandMasteringPhysics,andprintouts onthefronttable.  LectureNotes:PostedonMasteringPhysics  Typicallypostednightbeforeclassthenre‐postedwithannotations afterclass.  Recitation2:Jan28(NorecitationJan22becauseoftheholiday)  Onlyattendsectionyouregisteredfor.  Homework1: MustregisterforcourseinMasteringPhysics  Availablenow;duenextFriday(Jan25)by11PM  CourseID=MPCAPUANO191  Labs:Allstudentsmustregisterforalabsection!  FirstlabswillbeonJan30,31,Feb1.  Onlyattendthesectionyouregisteredfor.  PurchaseLabManualfromVirginiaBookCo(900W.Franklin)

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Last time: Electric Charge  BasicChargeModel:  Rubbinganobjectcancausetheobjecttobecomecharged  Twotypesofcharge:positive andnegative  Objectswiththesametypeofchargerepelwhilethosewith oppositechargeattract.  Theattractive/repulsiveforceisalong‐range force  Allobjectscontaincharge.Ifanobjectisneutral,itcontainsan equalamountofpositiveandnegativecharge.  AtomsandCharge: Chargeisanintrinsicpropertyofmatter  Atomsconsistofnegatively chargedelectronsorbitingapositive nucleus.  Sinceeverythingcontainscharge,allobjectscanexperiencethe electrostaticforce.  Note:Thesamecannotbesaidformagnetism!

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Atoms and Electricity  Theatomisheldtogetherbytheattractiveelectricforce betweenthepositiveprotonsinthenucleusandthenegative electrons.  Electronsandprotonshavechargesofoppositesignbut exactlyequalmagnitude.  Thisatomic‐levelunitofcharge,calledthefundamentalunit ofcharge,isrepresentedbythesymbole. 

 Unitofcharge:  Coulomb(C)  Derivedusingcurrent  Arodchargedto  has excess protons.

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Charge Quantization  Amacroscopicobjecthasnetcharge:

where  and  arethenumberofprotonsandelectrons containedintheobject.  Neutralvs.Charged:  Neutralobjectshaveequalnumbersprotonsandelectrons  Chargedobjectshaveunequalnumbersofprotonsand electrons.  Notefromtheaboveequationthatanobject’schargewill alwaysbeanintegermultipleof . Thisiscalledchargequantization. 4

Charge Quantization  Question1: Anatomhas31protonsand30electrons.Whatisthenet charge ofthisatom?  

         .       .    

 Question2:  electronsareremovedfromaneutralobject.Whatis thenetcharge ofthisobjectnow? (AnswerinunitsofμC  10 C)           .    /  .      .     ⇒   .  5

Charging and Discharging  Inourearlierexample,rubbingtheplasticrodwithwoolledtothe rodbecomingcharged.Whathappened?  Wedidnot“create”charge– wesimplytransferredcharges fromoneobjecttotheother.  Chargeconservation  Ingeneral:Touchingtwounlike objectstogethercauseschargesto movebetweenthem(Note:Wedon’thavetorubthemtogether!)  Example:staticelectricity  Whatishappening?  Electronsaremovingbetweentheobjects!  Somematerials“holdon”moretightlytotheirelectrons. 6

Static Electricity Electrons move to balloon, leaving net + charge on hair, net – charge on balloon

- - +

+ + +

Whatishappeninginthefigure?  Electrons movefromthehairtotheballoon.  Balloonbecomesnegatively charged  Hairbecomespositively charged  Oppositechargesattract:Hairstickstotheballoon  Likechargesrepel:Individualhairsrepeleachother 7

Insulators and Conductors Howanobjectischargedandhowitbehavesinthepresenceofexternal chargedependsontheobject’smaterial. Insulators:Electrons arealltightly boundtothepositivenuclei. Theseelectronscannotbeeasily detachedfromtheirnuclei.

Conductors:outeratomic electronsareonlyweakly boundtothenuclei. Ifdetached,theyarefreeto wanderaboutthroughthe entiresolid.

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Insulators and Conductors  Electronsarefreetomoveinconductorsbutnotininsulators.  Remember:Insolids,protonsdon’tmove. MetalNail (Conductor)

Charged

Neutral

Charged

Charged

WoodenMatch (Insulator)

Charged

Neutral

 Ifweconnecttwounequallychargedobjectswithaconductor, electronscanflowfreelybetweentheobjects.  Electronswillmoveuntiltheexcesschargeisevenlydistributed.  Ifweconnecttwounequallychargedobjectswithaninsulator,no chargewillflow.  Electronsarenotfreetomoveinaninsulator.

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Example: Motion of Charge (1)  Twospheres,onenegativeandoneneutral,areconnected byawireasshowninthefigure.Howdothechargesmove? a) Twoprotonsmovefromlefttoright b) Twoprotonsmovefromrighttoleft c) Twoelectronsmovefromlefttoright d) Twoelectronsmovefromrighttoleft Before:

negative

After:

neutral 10

Example: Motion of Charge (2)  Nowconsidertwosphereswithpositiveandoneneutral. Weconnectthemusingawireasshowninthefigure.How dothechargesmove? a) Twoprotonsmovefromlefttoright b) Twoprotonsmovefromrighttoleft c) Twoelectronsmovefromlefttoright d) Twoelectronsmovefromrighttoleft Before:

positive

After:

neutral 11

Example: Motion of Charge (3)  Goingbacktothefirstsituation,we startwithexcessnegativechargeon theleftsphere. Afterconnectingthewire,isit possibletohavetheconfigurationin thelowerfigure?

Before:

negative

neutral

After:

a) Yes b) No No– theelectronswillonlymoveuntil theexcesschargeisevenlydistributed. 12

Charging and Discharging Metalscan’tbechargedbyrubbing,insteadwechargebymaking contact.  Chargingbyconduction:  Rodmakescontact,transferringnegative chargetotheconductingcube.  Negativechargesrepeleachother,leading touniformdistributionofchargeacrossthe surfaceofthecube.  Discharging:  Touchingthecubewithanygrounded conductor(e.g.yourhand!)willcause chargetotransferfromthecubetoground. ⇒ Earthislarge– absorbsexcesscharge withoutbecomingchargeditself! 13

Charge Polarization Whatiftherodisbroughtnearthecubebutdoesn’tcomeinto contact?

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Polarization Force Thefigureshowsapositivelychargedrodnearaneutralpieceofmetal.  Themetalbecomespolarized  Topsurface=negative  Bottomsurface=positive  Thechargesintherodexertforcesonthemetal  Topsurface=attractive,upwardpointingforce  Bottomsurface=repulsive,downwardpointingforce  Thenetpolarizationforcepointstowardthechargedrod  Theelectricforcedecreases withdistance,so   and  pointsupward Question:Whydoesachargedrodpickuppiecesofpaper? 15

The Electric Dipole Consideranisolatedatom…  Theatomhasanequalnumberofprotonsandelectrons  Ithasneutral charge⇒   󰇛   󰇜  0  Bringa(+)chargenear:  Theelectronswillbeattracted tothecharge,thenucleuswill berepelledbythecharge.  Chargeseparation– theatomisstillneutral,butlocallythe lefthalfandrighthalfappearcharged.

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The Electric Dipole Whatifwehavemultipleatomsinaninsulator?  Whenaninsulatoris broughtnearanexternal charge,alltheindividual atomsinsidetheinsulator becomepolarized.  Thepolarizationforceacting oneachatomproducesa netpolarizationforce towardtheexternalcharge.

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The Electric Dipole Whathappensifwebringanegative externalchargenearour insulator? a) Theblockwillbeattracted.

???

b) Theblockwillberepelled.  Thenetpolarizationforcewillalwayspointtowardthe externalcharge.Canyouseewhy?

External charges

Atoms within the insulator

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QuickCheck 22.2 A rod attracts a positively charged hanging ball. The rod is A. Positive. B. Negative. C. Neutral. D. Either A or C. E. Either B or C.

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Quantifying the Force Between Charges  Whatdoweknowsofar?  Wecandefinetwotypesofcharge.  Positive&Negative  Scalarquantity  Units:Coulomb( )  Thereisalong‐rangeforcethatactsbetweencharges.  Likechargesrepel&unlikechargesattract  Wenowwishtoquantifythiselectrostaticforce.  Coulomb’sLaw– namedafterFrenchphysicistCharles‐ AugustindeCoulombwhostudiedelectricforcesinthe1780’s. 20

Coulomb’s Law – What did he do?  Usedatorsionbalancetodeterminerelationshipsbetweencharge, distanceandforce.  Simpletorsionbalance:  Hangarodfromathreadat itscenter.Thepropertiesof ourthreadareknown.  Exertaforceontherod, causingittotwistuntilit reachesanequilibrium position.  Measuretherotationangleof therod  Equilibrium:    21

Coulomb’s Law – What did he do?  Usedatorsionbalancetodeterminerelationshipsbetweencharge, distanceandforce.  Simpletorsionbalance:  Attachapositivelycharged spheretooneendoftherod.  Bringapositive“testcharge” neartherod.  Thechargesrepel,causingthe rodtorotate.  Measuretheangleofrotation  Howdoestheangle changewithchanging charge?

test charge

 Whataboutdistance? 22

Coulomb’s Law – What did he find?  Coulombdeterminedtworelationships:  Charge:Increasingchargeofeithersphereledtoincreased force

 Distance:Increasingdistanceledtodecreasedforce,obeying aninverse‐squarelaw

 Constantofproportionality:electrostaticconstant 





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Coulomb’s Law

point charges!

InSIunits  8.99   10 Nm /C  9  10 Nm /C

Convention: Wewilldenotetheforcesusingsubscriptssuchthat  isdefinedastheforce exertson and istheforce exertson 24...