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Electricity & Magnetism Lecture 1: Coulomb’s Law
Today’sConcepts:
A)Coulomb’sLaw
B)Superposi5on
Electricity&Magne5smLecture1,Slide1
Ifyouhaven'tdonePrelecture1yet,pleasedosolatertoday
Theforceonachargeduetoanotherchargeispropor5onaltotheproductofthechargesandinverselypropor5onaltothesepara5onsquared.
r
Theforceisalwaysparalleltoalineconnec5ngthecharges,butthedirec5ondependsonthesignsofthecharges:
q2
q2 q1
q1
Likesignsrepel
Coulomb’s Law:
q2 q1
OppositesignsaMractq2 q1
Electricity&Magne5smLecture1,Slide2
Taketwoballoonsandrubthembothwithapieceofcloth.A8eryourubthemtheywill:
A)A<racteach-otherB)Repeleach-otherC)Either–itdependsonthematerialofthecloth
Clicker Question: Balloons
Electricity&Magne5smLecture1,Slide3
Balloons
Ifthesamethingisdonetobothballoonstheywillacquirethesamesigncharge.
Theywillrepel!
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Electricity&Magne5smLecture1,Slide4
Text
We can only be sure about this if the balloons are made out of the same material.
Comment
Whatdoestherwithahatmean?Isitliketheunitvectorsi-hat,j-hatandk-hat,ordoesitmeansomethingelse?Thevideodidn'treallyexplainitthatwell.
Coulomb’s Law
Electricity&Magne5smLecture1,Slide5
Examples: Ifthechargeshavethesamesign,theforcebycharge1oncharge2wouldbeinthedirec5onofr12(totheright).
q2q1
Ifthechargeshaveoppositesign,theforcebycharge1oncharge2wouldbeoppositethedirec5onofr12(leT).
q1 q2
Ournota5on:
istheforceby1on2(think“by-on”)
istheunitvectorthatpointsfrom1to2.
Clicker Question: Coulomb Force
Whatwillthedirec5onoftheforcebe?
A)AMrac5ve B)Repulsive
k = 9 x 109 N m2 / C2
electroncharge= 1.6 x 10−19 Coulombs
NA = 6.02 x 1023
Twopaperclipsareseparatedby10meters.Thenyouremove1electronfromeachatomonthefirstpaperclipandplaceitonthesecondone.
Electricity&Magne5smLecture1,Slide6
Clicker Question: Coulomb Force
Whichweightisclosesttotheapproximateforcebetweenthosepaperclips(recallthatweight=mg,g=9.8m/s2)?
A)Paperclip(1 g x g)B)Textbook(1 kg x g)C)Truck(104 kg x g)D)AircraNcarrier(108 kg x g)
E)Mt.Everest(1014 kg x g)
k = 9 x 109 N m2 / C2
electroncharge= 1.6 x 10−19 Coulombs
NA = 6.02 x 1023
Twopaperclipsareseparatedby10meters.Thenyouremove1electronfromeachatomonthefirstpaperclipandplaceitonthesecondone.
Electricity&Magne5smLecture1,Slide7
CheckPoint: Forces on Two Charges
Electricity&Magne5smLecture1,Slide8
Two charges q = + 1 µC and Q = +10 µC are placed near each other as shown in the figure.Which of the following diagrams best depicts the forces acting on the charges:
CheckPoint Results: Forces on Two Charges
Electricity&Magne5smLecture1,Slide9
“Thebiggerchargewillpushthesmallerchargeharderthanthesmallerwillpushthelarger.“
“Theybothrepeleachother,andaccordingtotheF=kQq/r^2andnewton'sthirdlaw,theforceshavetobethesame.”
“Theforcesoftwoobjectsarealwaysequalandopposite.bothequasionsinvolvethechargeofbothparYclesinthesamemanner,thereforetheyarethesame..”
Two charges q = + 1 µC and Q = +10 µC are placed near each other as shown in the figure.Which of the following diagrams best depicts the forces acting on the charges:
q1
q2
q3
q4
Iftherearemorethantwochargespresent,thetotalforceonanygivenchargeisjustthevectorsumoftheforcesduetoeachoftheothercharges:
F2,1
F3,1
F4,1
F1
Superposition
Electricity&Magne5smLecture1,Slide10
F2,1
F3,1
F4,1
F1
WhathappenstoForceonq1ifitssignischanged?
A)|F1| increases
B)|F1| remainsthesame
C)|F1| decreases
D)NeedmoreinformaYontodetermine
Clicker Question: Superposition
q1
q2
q3
q4
Electricity&Magne5smLecture1,Slide11
Thedirec5onofallforceschangesby180o–themagnitudesstaythesame:
F2,1
F3,1
F4,1
F1
F2,1
F3,1
F4,1
F1
F2,1
F3,1
F4,1
F1
q1
q2
q3
q4
F2,1
F3,1
F4,1
F1
q1
q2
q3
q4
Electricity&Magne5smLecture1,Slide12
Electricity&Magne5smLecture1,Slide13
−Q +Q
+Q+Q
Case 1 Case 2
Comparethemagnitudeofthenetforceonqinthetwocases.
A)|F1| > |F2|
B)|F1|= |F2|
C)|F1|< |F2|
D)Dependsonsignofq
F1F2 = 0
Incaseone,bothoftheforcesareworkinginthesamedirecYon(thedownwarddirecYon)resulYnginagreaternetforceasopposedtocasetwowheretherepellingforcesareworkinginoppositedirecYonsinturncancelingeachotheroutBothcaseshaveachargedplacedequidistantfromchargesofthesamemagnitudessonoma[erchargeqhastheforcesatthisinstantarethesame.Themagnitudeofchargeofanelectronisthesameasthemagnitudeofaproton.So,whilethedistanceisthesame,themagnitudeofForcebetweenbothcaseswillbethesame.
CheckPoint: Compare Forces
CheckPoint: Compare Forces
−Q +Q
+Q+Q
Case 1 Case 2
Comparethemagnitudeofthenetforceonqinthetwocases.
A)|F1| > |F2|
B)|F1|= |F2|
C)|F1|< |F2|
D)Dependsonsignofq
F1F2 = 0
Incaseone,bothoftheforcesareworkinginthesamedirecYon(thedownwarddirecYon)resulYnginagreaternetforceasopposedtocasetwowheretherepellingforcesareworkinginoppositedirecYonsinturncancelingeachotherout
Bothcaseshaveachargedplacedequidistantfromchargesofthesamemagnitudessonoma[erchargeqhastheforcesatthisinstantarethesame.Thereisnowaytotelliftheforcesonthecenterchargearerepulsiveora[racYvewithoutknowingthesignofthecentercharge.
Electricity&Magne5smLecture1,Slide14
Force from Four Charges
Fourchargedpar5clesareplacedasshown.Apar5clewithcharge+Qisplaced1/2waybetweenthemiddle+qontheleTandthe+3qontheright
Whatisthedirec5onofhorizontalforceonQ?
A)leftwardB)noneC)rightward
x
y
3qq
q
q
Q
Electricity&Magne5smLecture1,Slide15
CheckPoint Results: Force from Four Charges
Fourchargedpar5clesareplacedonacircularringwithradius3masshownbelow.Apar5clewithchargeQisplacedinthecenterofthering
Whatisthedirec5onofhorizontalforceonQ?
A)Fx>0B)Fx=0C)Fx<0
x
y
3q
q qq
Q
Electricity&Magne5smLecture1,Slide16
Clicker Question: Force from Four Charges
Fourchargedpar5clesareplacedonacircularringwithradius3masshownbelow.Apar5clewithchargeQisplacedinthecenterofthering
Whatisthever&calforceonQ?
A)Fy>0B)Fy= 0 C)Fy<0
Fywouldequal0ifall3ofthebo[omchargeswereontopofeachother,butbecausetheyarepullingatanangle,theywillnotequaltheforceofthe3qchargethatispullingonlyinthe+YdirecYon.
They-direcYoncomponentsalsocanceleachotheroutsincethereisachargeorforceof3QpoinYngbothupwardanddownward.
ThetwoqchargesonthesidealsohaveanxcomponentsotheirFyisnotasgreatthusthesumoftheforcefromthebo[omchargesinsmallerthanthetopcharge.TheforcesarerepulsivesothechargewillhaveanegaYveFy.
x
y
Electricity&Magne5smLecture1,Slide17
3q
Q
q