18.1 Origin of Electricity 18.2 Charged Objects and Electric Force

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1 Oigin of lecticity 18. Chaged Objects and lectic Foce Thee ae two kinds of electic chage: positive and negative. The SI unit of electic chage is the coulomb (C). The magnitude of the chage on an electon o a poton is e C. The symbol e denotes a magnitude, it has no algebaic sign. Thus, the electon caies a chage of e, and the poton caies a chage of e. Macoscopic objects ae usually neutal. They acuie a net chage by losing () o gaining ( ) excess electons. Chage is neithe ceated not destoyed. Total chage in an isolated system is conseved Like chages (same sign) epel and opposite chages (opposite sign) changes attact: this is a Newtonian foce that obeys Newton s laws including the Thid Law: foces between two chaged paticles ae eual and opposite

2 18.3 letical conductos and insulatos 18.4 Chaging 18.5 Coulomb s Law lectical conductos ae mateials of vey low esistivity (ρ 10 8 Ωm) lectons ae fee to flow in the mateial In Static situations: No fee chages in the bulk inteio of the conducto Fee chages accumulate on the suface of the conducto lectical insulatos ae mateials of high esistivity (ρ Ωm) lectons not fee to flow in mateial Can chage object by contact o induction Contact will spead chages evenly ove identical conducting objects Chaging by induction is tempoay unless you then gound pat of the object fo a moment to emove excess chage on one side. Coulomb s Law Foce between point chages (eual and opposite) has magnitude Coulomb s constant: k N m /C k 1 Same sign: epulsion: foce on 1 is diectly away fom F Opposite sign: foce on is diectly towad F hee is the magnitude, so we put absolute value signs aound the chages. is the distance between 1 and

3 Coulomb s Law F ab is the foce exeted on a by b F F ij ij k i ij j F F F k ε ο 1 1 k 9 ( 4πε ) N m C o C ( N m ) F F lectic foces add as vectos! ( N m C )( C )( C ) 1 1 k 1 ( 0.15m) ( N m C )( C )( C ) k 13 ( 0.10m) F x F cosθ F cosθ 1 13 o o (9.59 N) cos(73 ) (17.95 N) cos(0 ).80 N N 0.75 N F y F sinθ F sinθ N N o o (9.59 N)sin(73 ) (17.95 N)sin(0 ) 9.17 N N 3 3

4 lectic Field and 18.7 Field Lines Static electic foce can be thought of in following tems: F Chage distibutions set up electic fields (a vecto values function of location) test chage 0 feels foce due to this field: lectic field is the foce that WOULD be felt by a test chage 0 divided by the test chage 0 1 lectic field due to a point chage: F Magnitude given by Coulomb s Law Points diectly away fom chage Points dictly towad chage Paallel Plate capacito: ach plate has aea A, the positive plate has chage, the negative has. distibuted unifomly ove the plates The electic field points pependiculaly fom the positive to the negative plate, has unifom/constant magnitude (this is an appoximation that neglects the edges) lectic fields add as vectos k 0 σ ε 0 ε 0 A 0

5 lectic Field due to point chage : k Field vectos point away fom chage and towad chage lectic fields fom diffeent souces add as vectos. A B Field lines flow out of chage and into chage Paallel plate capacito Suface chage density(chage/aea) ε o A σ ε o ε ο C ( N m ) 5

6 18.8 lectic Field inside conductos 18.9 Gauss s Law xcess chage esides on the suface of a conducto at euilibium unde electostatic conditions. In such a situation, the electic field at any point within the conducting mateial is zeo the electic field just outside the conducting suface is pependicula to the suface. lectic field inside empty cavities is zeo Gauss s Law: ( ) Φ cosφ A Q ε lectic flux out of an (imaginay) Gaussian suface Application of Gauss s Law: lectic field of a unifom line chage kλ λ Q πε 0 πε 0L o Total enclosed chage SI Units of lectic Flux: N m /C pependicula distance fom the line λ linea chage density 6

7 19.1 lectical Potential negy (P) 19., 19.3 lectic Potential Diffeence lectic foce is consevative The wok W AB, done by the electic field on a positive test chage 0 fom point A to point B, euals the electic potential enegy (P) at A minus that at B: This wok is path independent because the electostatic field is a consevative field lectical potential is defined as follows: In the move fom A to B unde the influence of an electic field, a test chage 0 expeiences a change in electical potential V V B V A - W AB / 0 (unit: volt VJ/C) lectic potential enegy of a test chage is P 0 V (unit: joules) Both eletic potential (V) and electic potential enegy (P) have abitay zeo efeence point A point chage geneates an electic potential given by Refeence zeo is at infinity V Positive chages acceleate fom egion of highe potential to lowe potential. Negative chages acceleate fom lowe V to highe V lectical potential enegy is pat of the conseved total enegy k ω P mv I mgh kx... 7

One electon volt is the magnitude of the amount by which the potential enegy of a poton o an electon changes when the electon moves though a potential diffeence of one volt. 1eV 1.

8 One electon volt is the magnitude of the amount by which the potential enegy of a poton o an electon changes when the electon moves though a potential diffeence of one volt. 1eV V J k With the field geneated by point chages: the electic field, foce, and acceleation NOT constant CANNOT use constant acceleation kinematics Must use consevation of enegy ***Special case of unifom cicula motion v m k 0 0 v 19.6 uipotential Suface and the electic field Fo this paallel plate capacito: V(y)y V s The electic field (component) in a given diection is eual to the ate of decease (with espect to space) of the electic potential in that diection Between paallel plate capacitos: potential inceases LINARLY towad the positive plate The electic field is constant constant foce on a test chage constant acceleation: Paticle motion poblems can be solved by kinematics of constant acceleation, OR by 8 consevation of enegy

9 19.7 Capacitos and Dielectics Capacitos: Modeled on paallel conducting plates of aea A (each) Spacing d Take chage fom side and move to side Develops electic field Potential diffeence (fom to side)

9 Capacitos and Dielectics Capacitos: Modeled on paallel conducting plates of aea A (each) Spacing d Take chage fom side and move to side Develops electic field Potential diffeence (fom to side) is Vd Capacito filled with ai/vacuum d ε 0 A V d C ε A V d 0 /( ε 0 A) Dielectics: dielectic constant κ Alignment of chages educes electic field gap filled with it by a facto of κ d ( κ ) ε 0 A V d C ( κ ) ε A V d 0 Definition of capacitance C SI Unit: faad FC/V V negy stoed in a capacito: U ½CV ½ /C ½V negy density stoed in electic field: u U/volume ½κε 0

10 Potential enegy of a system of point chages We stat with thee point chages: 1,, 3 U U 1 U13 U 3 k1 U k1 U U 3 U The oveall potential enegy is the amount of wok euied of an extenal agent to assemble this set of chages this can be done in diffeent ways, fo example: (a) Bing in 1 fom (no cost), W 1 0 (b) Bing in fom : W U 1 (c) Bing in 3 fom : W 3 U 13 U 3 Total W 1 W W UU 1 U 13 U 3 ij k k 3 i 3 ij j Can do this in any ode and obtain the SAM esult xtending to N point chages k N i 1 i j 1 U i 1 j ij j i ki ij j This is the same facto of ½ in the enegy stoed in a capacito 1 Thee ae N(N-1)/ distinct pais 10

11 Chapte 0 lectic Cicuits 11

plumbing ) Moden powe gid AC Tubine geneatos (Ch.

12 1 Since the 1950 s, people have associated advanced civilization with the use of electical powe (and indoo plumbing ) Moden powe gid AC Tubine geneatos (Ch..7) AC Altenating cuent kv AC Powe tansfomes: (Ch..9) V

electic potential enegy of chage caies by each Woking device: Convets enegy

13 0.1 lectomotive Foce and Cuent DC lectic Powe Souce I I R Woking Device A typical DC cicuit DC Diect I schematic diagam I Cuent Powe Souce: Boosts electic potential enegy of chage caies by each Woking device: Convets enegy caied by chages into wok, heat o othe foms of enegy I Cuent: flow of chage I 13

0.1 lectomotive Foce and Cuent Typical ca battey: 6 x V lead-acid cells 1V

(positive) chage caies ae aised Units: volts Both ae exothemic eactions

of chage pe unit time passing though a suface motion of chages.

one coulomb pe second: 1 A 1 C/s I Diect Cuent (DC): Chages move in the

14 0.1 lectomotive Foce and Cuent Typical ca battey: 6 x V lead-acid cells 1V Symbol fo a DC voltaic cell electomotive foce (emf) Potential by which the (positive) chage caies ae aised Units: volts Both ae exothemic eactions Symbol fo a multi-cell battey (showing 5 cells) The electic cuent amount of chage pe unit time passing though a suface motion of chages. Cuent t One ampee (A o amp). one coulomb pe second: 1 A 1 C/s I Diect Cuent (DC): Chages move in the same diection at all times If the chages move fist one way and then the opposite way, the cuent is said to be altenating cuent (AC). 14

0.1 lectomotive Foce and Cuent Conventional cuent is the hypothetical flow of positive chages that would have the same effect in the cicuit as the movement of negative chages (electons) that actually

15 0.1 lectomotive Foce and Cuent Conventional cuent is the hypothetical flow of positive chages that would have the same effect in the cicuit as the movement of negative chages (electons) that actually does occu in the opposite diection. xample A Pocket Calculato The cuent in a 3.0V battey of a pocket calculato is I0.17mA. In one hou of opeation, (a) how much chage flows in the cicuit and, (b) how much enegy does the battey delive to the calculato cicuit? 15

16 0.1 lectomotive Foce and Cuent Conventional cuent is the hypothetical flow of positive chages that would have the same effect in the cicuit as the movement of negative chages (electons) that actually does occu in the opposite diection. xample A Pocket Calculato The cuent in a 3.0V battey of a pocket calculato is I0.17mA. In one hou of opeation, (a) how much chage flows in the cicuit and, (b) how much enegy does the battey delive to the calculato cicuit? (a) I ( t) ( A)( 3600 s) 0.61C e e e e (b) negy Chage ( V ) ( 0.61C)( 3.0 V) 1.8 J negy Chage 16

Those mateials we use to connect cicuit elements (wies/cables/taces) have vey low esistance (geneally not measuable

17 0. Ohm s Law I Symbol fo a multi-cell battey (showing 5 cells) I Ohm s Law V I I V R Resistance, V IR, o Conductos in geneal obey Ohm s Law. Those mateials we use to connect cicuit elements (wies/cables/taces) have vey low esistance (geneally not measuable with hand-held metes). We geneally teat them as if they have no esistance at all. The components with measuable esistances ae efeed to as esistos I V R SI Unit of Resistance: volt/ampee (V/A) ohm (Ω) Symbol fo a esisto R 17

18 0. Ohm s Law xample: Flashlight The filament in a light bulb is a esisto in the fom of a thin piece of wie. The wie becomes hot enough to emit light because of the cuent in it. The flashlight uses two 1.5-V batteies (stacked in seies) to povide a cuent of 0.40 A in the filament. Detemine the esistance of the glowing filament. 18

0. Ohm s Law xample: Flashlight The filament in a light bulb is a esisto in the fom of a thin piece of wie. The wie becomes hot enough to emit light because of the cuent in it.

19 0. Ohm s Law xample: Flashlight The filament in a light bulb is a esisto in the fom of a thin piece of wie. The wie becomes hot enough to emit light because of the cuent in it. The flashlight uses two 1.5-V batteies (stacked in seies) to povide a cuent of 0.40 A in the filament. Detemine the esistance of the glowing filament. R NOT: (1) V V V u V d specifically the upsteam potential minus the downsteam potential V I 3.0 V 0.40 A 7.5 Ω () Potential is measued at ON point on the cicuit. Potential diffeence is measued between TWO points in a cicuit. (3) Cuent is measued THROUGH a continuous segment of a cicuit (i.e. no banch points) V u V V R I V d 19

Review for Midterm-1

Review for Midterm-1 Review fo Midtem-1 Midtem-1! Wednesday Sept. 24th at 6pm Section 1 (the 4:10pm class) exam in BCC N130 (Business College) Section 2 (the 6:00pm class) exam in NR 158 (Natual Resouces) Allowed one sheet