PHYS 219 Spring semester Lecture 02: Coulomb s Law how point charges interact. Ron Reifenberger Birck Nanotechnology Center Purdue University

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1 PHYS 19 Spring semester 016 Lecture 0: Culmb s Law hw pint charges interact Rn Reifenberger Birck Nantechnlg Center Purdue Universit Lecture 0 1 Earl Develpments in Electrstatics Tw f the ur rces in Nature: Gravit Electrmagnetic The electrmagnetic frce is man, man rders f magnitude strnger than gravitatinal frces. In mst circumstances, the electrmagnetic frce acting n macrscpic bjects is essentiall zer because psitive and negative charges are clsel paired with each ther. Classical electrstatics is all abut redistributing small amunts f charge! 1

2 Review Atmic Ther f Matter Size f atm ~ 0.1 nm r m Nt t scale! e n P p p n e p n p e Electricall Neutral Atm e e smbl charge mass neutrn prtn electrn n P e 0 (zer) C C kg kg kg Nte: 1 C = 1 Culmb 3 implicatins Mre realistic picture Eample : Sdium in Eample 1: Carbn atm Net Charge = 0 Net Charge = +1 e Nt t scale! 4

3 An electrn (r a prtn) has a measured charge f magnitude e = Culmbs. This means apprimatel (6,50,000,000,000,000,000) electrns r prtns are reuired t make ne Culmb (1 C) f charge. EXAMPLE: Everda matter cntains an unbelievabl large number f electrns and prtns. r instance, a 1 cm 3 piece f aluminum cntains Al atms. Each Al atm cntains 13 electrns. S there are electrns in a 1 cm 3 blck f Al and eactl the same number f prtns. When an bject has the same number f electrns and prtns, it has n net charge and it is electricall neutral. Charging an bject 5 Hw d bjects becme charged? The additin r remval f electrns t an bject creates negativel and psitivel charged bjects. Ecept under etreme cnditins, prtns sta in place and electrns are transferred. Ver simple eample: Determine the net charge n the bject? + = 1e = 1p Ans: 3e = 3 ( C)= C Hw was a net charge n this bject created? Three clicks 6 Ke Pint 3

4 Ke Pints Charge is said t be uantized, itisalwas bserved as an integer multiple f e, the magnitude f the charge f ONE electrn r ONE prtn. Charge can be redistributed, but nt created r destred. An bject is charged when it has an imbalance between electrns and prtns. 7 Cnservatin f Charge Electric charge is cnserved. The net charge f an islated sstem ma be psitive, negative r zer. Charge can mve between bjects in a sstem, but the net charge f an islated sstem remains unchanged. Cnductrs, Insulatrs, Grund Cnductr: An bject r material in which charge can flw relativel freel metals. Insulatr: An bject r material in which charge des nt flw freel dielectrics r insulatrs. Electrical Grund: Grund is the name given t an large cnducting bject, like a metallic water pipe in a building, that is usuall cnnected t earth. We then sa that charge flws frm a charged bject t a grund reservir, leaving the bject electricall neutral. Imprtance f electrical grund in high vltage music: see (scrll t end f vide) 8 4

5 Charging b rictin an Imprtant Eample balln Apprach wall fur balln frictin rub balln with fur wall 9 Trib Series 10 5

6 Practical Cnsideratins rictinal Charging What lses electrns? What gains electrns? Charges psitive Tp rller Charges negative Bttm rller 11 Inducing an electric charge withut direct cntact Case 1. Electrical behavir f a cnductr (metal) Cnsider a cnducting rd suspended b tw strings. strings Imprtant Pints The cnducting rd becmes highl POLARIZED. The cnducting rd is still electricall neutral. strings 1 Inducing charge n insulatr 6

7 Inducing an electric charge withut direct cntact Case. Electrical behavir f an insulatr (r dielectric) BEORE ATER dielectric (insulating) slab negativel charged rd The dielectric becmes lcall POLARIZED. The dielectric bject is still electricall neutral Balln n wall What are the cnseuences f net charge? Electrstatic rce Ke Idea: The Net Charge n an bject is imprtant. 14 attractive r repulsive? 7

8 Electrstatic rces can be repulsive r attractive The frces act alng a straight line between the centers f tw pint charges Like charges repel; Unlike charges attract 15 Inducing charge A rce is a Push r a Pull. rce is measured in Newtns. Bth gravit and electrstatic frces are nncntact frces. The act n bjects that d nt tuch each ther. Gravitatinal rce g m 1 r m m m 1 g G r Electrstatic rce e e k 1 r 1 k = Nm /C G = Nm /kg 16 r 8

9 The Electrstatic rce: Culmb s Law Pint charges ONLY! The charges are stuck dwn! e k 1 k = Nm /C Nm /C r rce is a vectr! It has a directin! Need a crdinate sstem! 17 sample prblem Make sure u knw hw big is 1 Newtn and 1 Jule 1N weight f 100 gm (0.1 kg) n earth weight f ~1 range If u can lift 100 lbs, u are eerting a frce f ~ 446 N If u mve100 gm thrugh1 m n earth, u d1 J f wrk hand gravit =mg =0.1 kg 9.98 m/s =abut 1N hand = 1 N hand 1 m Wrk = 1 N m = 1 J 18 9

10 Eample: Tw grains f pllen have a charge f +1 nc. If the are lcated 3 cm apart, what is the electrstatic frce acting n each? 3 cm = 0.03 m +1 nc +1 nc =k 1 e r = Nm /C 9 5 = N; repulsive C 0.03m Nte: 1 nc=1 nanculmb=110 9 C (see metric prefies listed in lecture 1) 19 Up Net: Electrstatic Ptential Energ Please read the Appendi t this lecture which reviews situatins invlving mre than TWO charges. 0 10

11 APPENDIX: Principle f Superpsitin Applied t Culmb s Law Q: Since Culmb s Law nl invlves TWO pint charges, what happens when mre than tw pint charges are present at ne time? A:Sincefrceisavectr,thettalfrceeertedna particular charge is the vectr sum f all the individual frces acting n that charge. This is ften called the Principle f Superpsitin. vectrcmpnents.html 1 I. The Additin f Vectrs (Graphical) Three frces acting n an bject. What is Net rce? 1 click 1 net 3 3 The rder that the vectr additin is perfrmed des nt matter! net 3 1 click 11

12 II. The Additin f Vectrs (Numerical) Yu need t define a crdinate sstem. a) b) 1 3 c) 3 3 KEY IDEA: Add the vectr cmpnents alng each directin One click 3 Net: a numerical eample 3 III. An eample What is frce n 1? 1 1 Sstem f 3 pint charges cs( ) 3 1 in directin There are TWO frces ( 1 and ) acting in DIERENT directins sin( ) 3 1 in + directin 4 1

13 Reslving the frces int their cmpnents 1 1 subtract = 1 net 5 Eample: What is frce n 1? (si steps) A. Units: 10 cm = 0.1 m 1.00 C = C C. rce Diagram 30 Assign the apprpriate directins! B. Gemetr m m m

14 D. Vectr Cmpnents sin(30 ); cs(30 ); sin(30 ); cs(30 ); E. Arithmetic 1 1 k r k r N 0.1. inal Answer net 1 net 1 0.9Nsin(30 ) 0.9Nsin(30 ) 0.90N in + directin 0.9Ncs(30 ) 0.9Ncs(30 ) 0.00N in directin N 7 D NOT Becme Cnfused Abut Plarit f Charges! (same prblem with fur different chices fr charge plarit)

15 In summar, the Principle f Superpsitin states that fr frces 1,, 3,... n n... net m 1 3 n m1 It s a vectr sum!!!! 9 15