Electricity & Magnetism Lecture 1: Coulomb’s Law

Today’sConcepts:

A)Coulomb’sLaw

B)Superposi<on

Electricity&Magne<smLecture1,Slide1

Ifyouhaven'tdonePrelecture1yet,pleasedosolatertoday

Ancient Greece

Amber: ήλεκτρον (made by the sun, “electron”)

Taketwoballoonsandrubthembothwithapieceofcloth.AKeryourubthemtheywill:

A)ALracteach-otherB)Repeleach-otherC)Either–itdependsonthematerialofthecloth

Clicker Question: Balloons

Electricity&Magne<smLecture1,Slide3

Balloons

Ifthesamethingisdonetobothballoonstheywillacquirethesamesigncharge.

Theywillrepel!

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Electricity&Magne<smLecture1,Slide4

Text

We can only be sure about this if the balloons are made out of the same material.

Theforceonachargeduetoanotherchargeispropor<onaltotheproductofthechargesandinverselypropor<onaltothesepara<onsquared.

r

Theforceisalwaysparalleltoalineconnec<ngthecharges,butthedirec<ondependsonthesignsofthecharges:

q2

q2 q1

q1

Likesignsrepel

Coulomb’s Law:

q2 q1

OppositesignsaLractq2 q1

Electricity&Magne<smLecture1,Slide2

Comment

Whatdoestherwithahatmean?Isitliketheunitvectorsi-hat,j-hatandk-hat,ordoesitmeansomethingelse?Thevideodidn'treallyexplainitthatwell.

Coulomb’s Law

Electricity&Magne<smLecture1,Slide5

Examples: Ifthechargeshavethesamesign,theforcebycharge1oncharge2wouldbeinthedirec<onofr12(totheright).

q2q1

Ifthechargeshaveoppositesign,theforcebycharge1oncharge2wouldbeoppositethedirec<onofr12(leK).

q1 q2

Ournota<on:

istheforceby1on2(think“by-on”)

istheunitvectorthatpointsfrom1to2.

Clicker Question: Coulomb Force

Whatwillthedirec<onoftheforcebe?

A)ALrac<ve B)Repulsive

k = 9 x 109 N• m2 / C2

electroncharge= 1.6 x 10−19 Coulombs

NA = 6.02 x 1023

Twopaperclipsareseparatedby10meters.Thenyouremove1electronfromeachatomonthefirstpaperclipandplaceitonthesecondone.

Electricity&Magne<smLecture1,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)AircraKcarrier(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&Magne<smLecture1,Slide7

CheckPoint: Forces on Two Charges

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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&Magne<smLecture1,Slide9

“Thebiggerchargewillpushthesmallerchargeharderthanthesmallerwillpushthelarger.“

“Theybothrepeleachother,andaccordingtotheF=kQq/r^2andnewton'sthirdlaw,theforceshavetobethesame.”

“Theforcesoftwoobjectsarealwaysequalandopposite.bothequasionsinvolvethechargeofbothpar<clesinthesamemanner,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:

Your Reasons

q1

q2

q3

q4

Iftherearemorethantwochargespresent,thetotalforceonanygivenchargeisjustthevectorsumoftheforcesduetoeachoftheothercharges:

F2,1

F3,1

F4,1

F1

Superposition

Electricity&Magne<smLecture1,Slide10

F2,1

F3,1

F4,1

F1

WhathappenstoForceonq1ifitssignischanged?

A)|F1| increases

B)|F1| remainsthesame

C)|F1| decreases

D)Needmoreinforma<ontodetermine

Clicker Question: Superposition

q1

q2

q3

q4

Electricity&Magne<smLecture1,Slide11

Thedirec<onofallforceschangesby180°–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&Magne<smLecture1,Slide12

CheckPoint: Compare Forces

qq

−Q +Q

+Q+Q

Case 1 Case 2

Comparethemagnitudeofthenetforceonqinthetwocases.

A)|F1| > |F2|

B)|F1|= |F2|

C)|F1|< |F2|

D)Dependsonsignofq

F1F2 = 0

Incaseone,bothoftheforcesareworkinginthesamedirec<on(thedownwarddirec<on)resul<nginagreaternetforceasopposedtocasetwowheretherepellingforcesareworkinginoppositedirec<onsinturncancelingeachotherout

BothcaseshaveachargedplacedequidistantfromchargesofthesamemagnitudessonomaLerchargeqhastheforcesatthisinstantarethesame.ThereisnowaytotelliftheforcesonthecenterchargearerepulsiveoraLrac<vewithoutknowingthesignofthecentercharge.

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Force from Four Charges

Fourchargedpar<clesareplacedasshown.Apar<clewithcharge+Qisplaced1/2waybetweenthemiddle+qontheleKandthe+3qontheright

Whatisthedirec<onofhorizontalforceonQ?

A)leftwardB)noneC)rightward

x

y

3qq

q

q

Q

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CheckPoint Results: Force from Four Charges

Fourchargedpar<clesareplacedonacircularringwithradius3masshownbelow.Apar<clewithchargeQisplacedinthecenterofthering

Whatisthedirec<onofhorizontalforceonQ?

A)Fx>0B)Fx=0C)Fx<0

x

y

3q

q qq

Q

Electricity&Magne<smLecture1,Slide16

Clicker Question: Force from Four Charges

Fourchargedpar<clesareplacedonacircularringwithradius3masshownbelow.Apar<clewithchargeQisplacedinthecenterofthering

Whatisthever&calforceonQ?

A)Fy>0B)Fy= 0 C)Fy<0

Fywouldequal0ifall3oftheboLomchargeswereontopofeachother,butbecausetheyarepullingatanangle,theywillnotequaltheforceofthe3qchargethatispullingonlyinthe+Ydirec<on.

They-direc<oncomponentsalsocanceleachotheroutsincethereisachargeorforceof3Qpoin<ngbothupwardanddownward.

ThetwoqchargesonthesidealsohaveanxcomponentsotheirFyisnotasgreatthusthesumoftheforcefromtheboLomchargesinsmallerthanthetopcharge.Theforcesarerepulsivesothechargewillhaveanega<veFy.

x

y

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3q

qq

Q

q