Lesson 14 Coulomb s Law

Transcription

1 Physics 30 Lsson 14 oulomb s Law I. Histoical dvlopmnt of oulomb s Law In 1775, n anklin notd that a small nutal cok hanging na th sufac of an lctically chagd mtal can was stongly attactd to th outsid sufac of th mtal can. Whn th sam nutal cok was lowd insid th can, th cok was not attactd to th sufac of th can. anklin was supisd to discov no attaction within th can but stong attaction outsid th can. Josph Pistly was a hous gust of n anklin in Pistly had bn studying scinc at ambidg, but had fld fom England bcaus of ligious pscution. anklin askd Pistly to pat his xpimnt. Pistly obtaind th sam sults as anklin, but th xpimnt tiggd mmois of Nwton s discussion of gavity within a hollow plant. Nwton had xamind th possibility of gavity insid a hollow plant in his book Pincipia Mathmatica Pincipls of Mathmatics. Nwton cam to th conclusion that any point insid th hollow plant would b subjct to focs fom th sufac but th focs would all cancl out laving th appaanc of no gavitational fild. Pistly asond that th appaanc of no nt lctical focs insid th mtal can might b vy simila to gavity within th hollow plant. Pistly suggstd that this xpimnt showd that lctical focs w vy simila to gavitational focs. hals oulomb ( ) was vy intigud by Pistly s intuitiv connction btwn lctostatic focs and gavitational focs. H immdiatly bgan to tst th lationship using a tosion balanc which was simila to a dvic that avndish had usd to masu th univsal gavitational constant G. H masud th foc of lctostatic pulsion using th tosion balanc as diagammd to th ight. If (b) and (a) hav lik chags thn thy will pl ach oth causing th od to which (a) is attachd to twist away fom (b). Th foc ncssay to twist th wi attachd to th od holding (a) could b dtmind by fist finding th lationship btwn th angl of tosion and th pulsiv foc. Thus, oulomb had a way to masu th foc of pulsion. oulomb thn bgan to tst th ffct of incasing th chag on both (a) and (b) and h found that th pulsiv foc incasd. Evntually h found that th lctostatic foc was dictly popotional to th poduct of th chag on ach objct. q 1 q q 1 chag on (b) q chag on (a) D. Ron Licht

2 oulomb thn tstd to s th ffct of incasing th distanc btwn (a) and (b) and found that th foc dcasd by th squa of th distanc btwn th two objcts. 1 distanc btwn chags (cnt to cnt) Whn oulomb combind th two lationships togth h found that th lctostatic foc vaid dictly as th poduct of th two chags and invsly as th squa of th distanc btwn th two chagd objcts. q q 1 ft patd masumnts wh th chags and distancs w known, h was abl to plac th popotionality sign with (k) which is known as oulomb s constant. 9 Nm k Th final sult is known as oulomb s Law of lctostatic attaction. qq k 1 Th lationship is vy simila to Nwton s Univsal Gavitation Law and th connction pdictd by Pistly s intuitiv lap was confimd. II. Using oulomb s Law Whn using oulomb s Law, th quation dos a gat job of calculating th magnitud of th foc, but it is not good at pdicting th diction of th foc. o xampl, consid two chags (+0 ) and (15 ) that a 0.5 m apat. Using oulomb s Law w can calculat th foc btwn and. qq k Nm ( 0 10 )( ) (0.5m) 43N Th magnitud of th foc is 43 N, but what dos th ngativ sign signify? Th Law of hags (s Lsson 13) stats that unlik chags attact. Thfo, in th contxt of this xampl, th ngativ sign indicats an attactiv foc btwn and. If and had th sam typ of chag, ith both positiv o both ngativ, oulomb s Law would poduc a positiv answ indicativ of a pulsiv foc. D. Ron Licht 14

3 Now consid a simila xampl wh th situation is diagammd to th ight and w a askd to calculat th foc acting on chag. Using oulomb s Law qq k Nm ( )( 110 ) (0.5m) 17N m 1 th magnitud of th foc btwn and is 17 N, but what dos th ngativ sign man in this contxt? t this point many studnts mak th mistak of dawing th foc vcto on in th ngativ (lft) diction. Incoct!!! 17 N Th Law of hags indicats that is attactd to, which, in th contxt of th givn situation, is in th positiv (ight) diction. +10 oct!!! 17 N 1 asd on th xampls abov, it is stongly commndd that oulomb s Law b usd to calculat th magnitud of th foc, whil th Law of hags and th spcific situation o contxt b usd to indicat th diction of th foc. Thfo, think of oulomb s Law as an absolut valu quation wh th signs of th chags a not impotant. 9 Nm 6 6 q q k (10 10 )(1 10 ) 17N (0.5m) Thn us th contxt of th qustion to dtmin th diction of th foc. D. Ron Licht

4 III. oulomb s Law and Nwton s 3 d Law In th xampl abov w w considing th lctostatic foc btwn and and w focussd ou attntion on chag. What if w had bn askd about th foc on chag? oulomb s Law indicats th sam magnitud of foc acts on and on, but th diction of th foc on would b to th lft sinc th ngativ is attactd to th positiv. This is an xampl of Nwton s 3 d Law i.. an action foc ( on ) is accompanid by a action foc ( on ) that is qual in magnitud and opposit in diction. In tms of poblm solving, it is ssntial that w focus on th focs acting on th chag of intst and to igno th action focs acting on th oth chag(s). You will lan mo about this in th xampls and assignmnt poblms blow. IV. Elctostatics xampl poblms N 17 N 1 Exampl 1 What is th lctostatic foc of attaction btwn a 8.0 x 10-6 chag and a +6.0 x 10-5 chag spaatd by m? qq 1 k 9 Nm ( )( ) (0.050m) oulomb s Law is usd to calculat th magnitud of th lctostatic foc. Th diction of th foc is dtmind by th Law of hags (lik chags pl, unlik chags attact). Sinc + and attact N = 1.7 x 10 N attaction Exampl fixd chag of +5.0 x 10-4 acts upon a 5.0 g mass which has a chag of +7.0 x If th chags a 0.50 m away fom on anoth, what is th acclation xpincd by th 5.0 g mass? qq 1 k a m Nm ( )( ) 1586N a (0.50m) kg N away fom th chag 4 a away fom m s D. Ron Licht

5 Exampl 3 If th foc btwn two qually chagd paticls is 9.0 x 10 6 N and th distanc btwn thm is 0.50 cm, what is th chag on ach paticl? q1 q qq 1 k q1 k 6 qq N(0.0050m) 1 1 k q 1 9 Nm q1-4 k q 1 q Exampl 4 Whn two chagd paticls a st a ctain distanc apat, a pulsiv foc of 8.0 N xists. What is th foc of pulsion btwn th two paticls if th distanc btwn thm is doubld and on of th chags is tipld in siz? In this solution, wit th quation and thn whatv is don to on sid is don to th oth sid as wll. qq 1 k 8.0N( 3) q1q ( 3) k ( ) 6.0N D. Ron Licht

6 Exampl chag and a +160 chag a st 9.0 m apat. n unknown positiv chag is placd on a lin joining th fist two chags and it is allowd to mov until it coms to st btwn th two chags. t what distanc masud fom th 160 chag will th unknown chag com to st? x Th chag will com to st wh th focs fom and on a qual to ach oth. k q q (9.0 x) k q q (9.0 x) x q q x (9.0 x) q x 40 x (9.0 x) 160 q 0.5x (9.0 x) (squa oot both sids) 0.50x 9.0 x 1.50x 9.0 x 6.0m (+) chag 9.0 m x +160 D. Ron Licht

7 om th diagam blow dtmin th nt lctostatic foc on m m d d 0.15m tan Th a two focs acting on chag : on and on. qq qq on k on k 9 Nm 6 6 on on ( )( ) (0.075m) 19.18N away fom Th f body diagam is: 4.60 N N 9 Nm 6 6 on on ( )( ) 4.60N towad (W) = 4.60 sin53.1 (N) = 3.68 wst (0.15m) W can add ths vctos togth by baking th 4.60 N foc into its noth and wst componnts o (N) = 4.60 cos53.1 (N) =.76 noth dding all of th componnts togth: (ast-wst) = 3.68 wst (noth-south) =.76 noth south = 16.4 south NET 16.4 N 3.68 N NET 16.8N NET tan 1.6 W of S NET o 16.8N 1.6 W of S D. Ron Licht

8 V. Pactic poblms 1. alculat th lctic foc btwn two point chags of 4.00 and 3.00 whn thy a.00 cm apat. (70 N pulsion). Two point chagd objcts poduc an lctic foc of N on ach oth. What is th lctic foc if th distanc btwn thm incass th tims and on of th chags is doubld? ( N) 3. Two point chags poduc a pulsiv foc of N whn placd m apat. What is th chag on ach point chag if th magnitud of th lag chag is th tims th magnitud of th small chag? (0.11, ) D. Ron Licht

9 4. om th diagam blow dtmin th nt lctostatic foc on chag. (19.9 N [16 o W of N]) m m Two small sphs, ach with a mass of.00 x 10-5 kg a hoizontally placd m apat. On sph has a chag of.00 and is fixd in position. Th oth sph has a chag of 3.00 and is f to mov. What is th initial acclation of th scond sph? (. x 10 4 m/s ) D. Ron Licht

10 VI. Hand-in assignmnt Pat Elctostatics visitd 1. How could a nutal insulatd mtal conducto b givn a ngativ chag using:. a ngativly chagd od?. a positivly chagd od? Us diagams to suppot you answ.. Why dos ubbing a conducto not poduc a static chag whas ubbing an insulato can poduc a static chag? 3. What is th nt chag on a mtal sph having an xcss of 1.0 x lctons? ( 1.6 x 10-9 ) 4. What is th nt chag on a mtal sph having a dficit of 1.0 x 10 1 lctons? (+1.6 x 10-7 ) 5. If a ngativly chagd od is bought na th knob of a positivly chagd lctoscop, what will happn to th spaation btwn th lavs of th lctoscop? Explain. 6. positivly chagd od is bought na an lctoscop that is alady chagd. If th lavs spad futh apat, what kind of chag dos th lctoscop hav? Explain. 7. Givn a solid mtal sph and a hollow mtal sph, ach with th sam adius, which will hold th gat chag? Justify you answ. 8. mtal sph with an xcss of 7.75 x potons is touchd to anoth idntical nutal mtal sph. What is th final chag on ach sph? (6. ) 9. Dscib two ways to giv a nutal lctoscop a positiv chag, using only a pic of silk and a glass od. ould th sam matials b usd to giv it a ngativ chag? If so, how? D. Ron Licht

11 Pat oulomb s Law poblms 1. ompa Nwton s Law of Univsal Gavitation with oulombs Law, pointing out th similaitis and diffncs.. ind th foc of lctostatics attaction btwn a +100 chag and a 5.00 chag locatd 50.0 cm apat. ( 18.0 N) 3. If th foc of attaction btwn two chags is 310 N, what will b th foc if on of th chags is mad fou tims lag and th distanc is ducd to half of its oiginal valu? ( 4.96 kn) 4. What chag q placd 4.0 cm fom a chag of 80 n will poduc a pulsiv foc of N? (3.3 x 10-8 ) 5. Two small mtallic sphs hav th sam mass and volum. On of th sphs has a chag of and th oth a chag of If th two sphs a bought into bif contact with ach oth and a thn spaatd to a distanc of 0.00 m, what is th lctic foc btwn thm? (0.506 N) 6. Two small, oppositly chagd sphs hav a foc of lctic attaction btwn thm of 1.6 x 10 - N. What dos this foc bcom if th chag on ach sph is halvd and thn thy a placd twic as fa apat as bfo? (1.0 x 10-3 N) 7. On modl of th stuctu if th hydogn atom consists of a stationay poton with an lcton moving in a cicula path aound it, of adius 5.3 x m. a) What is th lctostatic foc btwn th lcton and th poton? (8. x 10-8 N) b) What is th gavitational foc btwn thm? (3.6 x N) c) What is th atio of th lctostatic foc to th gavitational foc? (.3 x :1) d) Which foc is mainly sponsibl fo th lcton s cntiptal motion? ) alculat th vlocity and piod of th lcton s obit aound th poton. (. x 10 6 m/s, 1.5 x s) 8. Two small chags, +40 and 18, a placd 4 cm apat. What is th foc on a thid small chag, of magnitud.5, if it is placd on th lin joining th oth two, and a) 1 cm to th outsid of thm, on th sid of th ngativ on? (1 N away fom ngativ chag) b) 1 cm to th outsid of thm, on th sid of th positiv on? (59 N towad positiv chag) cm 18 D. Ron Licht

12 9. Two positiv chags 4.0 cm apat pl ach oth with a foc of 0.90 N. On of th chags is known to b fou tims lag than th oth chags. ind th magnitud of th lag chag. (8.0 x 10-7 ) 10. In th diagam blow, has a chag of +0.30, has a chag of -0.0 and has a chag of What is th nt foc on? (0.093 N [S]) 10 cm 10 cm 11. Th chags a placd as shown in th diagam blow. What is th nt foc on th +4.0 chag? ( o S of E) cm 0.60 m small ngativly chagd Styofoam ball lying on a tabl is pulld upwad fom th tabl at a constant spd by th lctostatic foc btwn it and anoth Styofoam ball hld.0 cm abov it. ssuming th balls hav th sam magnitud of chag and th sam mass (0.100 g), what is th smallst possibl chag on th ball on th tabl? (6.6 x 10-9 ) 13. Two positiv chags (+5.0 ) and (+0 ) a 1.0 cm apat. thid chag (+4.0 ) is placd in th lin btwn and and it is f to mov along th lin. t what point, masud fom, will chag com to st? (8 cm) *14. Two small, idntical, chagd sphs attact on anoth with a foc of 8.0 x 10-5 N, whn thy a 30 cm apat. Thy a touchd togth, and a again placd 30 cm apat, but thy now xt a foc of pulsion of 1.0 x 10-5 N on ach oth. a) What is th chag on ach sph aft thy a touchd? (1.0 x 10-8, sam signs) b) What was th chag on ach bfo thy w touchd? (4.0 x 10-8 and.0 x 10-8, opposit signs) 0.60 m D. Ron Licht