General Physics (PHY 2140)

Transcription

1 Geneal Physics (PHY 140) Intoduction Syllabus and teaching stategy lecticity and Magnetism Popeties of electic chages Insulatos and conductos oulomb s law Lectue: Office Hous: D. Alan A. Sebastian, Physics Building Phone: (to leave a message with a secetay) alansebastian@wayne.edu, Web: TBD, Physics Building,, o by appointment. Gading: Reading Quizzes bonus Quiz section pefomance/homewok 10% Best Hou xam 5% Second Best Hou xam 5% Final 40% Reading Quizzes: Homewok and QUIZ Sessions: Hou xams and Final xam: Online ontent: Syllabus and teaching stategy It is impotant fo you to come to class pepaed! The quiz sessions meet once a week; quizzes will count towads you gade. Thee will be THR (3) Hou xams and one Final xam. Lectues will be made available to you as a supplemental efeence. Lectue 1. hapte 15 1 Intoduction 15.1 Popeties of lectic hages Discovey Knowledge of electicity dates back to Geek antiquity (700 B). Began with the ealization that ambe (fossil) when ubbed with wool, attacts small objects. This phenomenon is not esticted to ambe/wool but may occu wheneve two nonconducting substances ae ubbed togethe. Obsevation of Static lecticity A comb passed though hai attacts small pieces of pape. An inflated balloon ubbed with wool. lectically chaged Rub shoes against capet/ca seat to chage you body. Remove this chage by touching anothe peson/a piece of metal. Two kinds of chages Named by Benjamin Fanklin ( ) 1790) as positive and negative. Like chages epel one anothe and unlike chages attact one anothe

2 15.1 Popeties of lectic hages Natue of lectical hage 15.1 Popeties of lectic hages Quantization Oigin of chage is at the atomic level. Nucleus : obust, positive. lectons : mobile, negative. Usual state of the atom is neutal. hage has natual tendency to be tansfeed between unlike mateials. lectic chage is howeve always conseved in the pocess. hage is not ceated. Usually, negative chage is tansfeed fom one object to the othe. Robet Millikan found, in 1909, that chaged objects may only have an intege multiple of a fundamental unit of chage. hage is quantized. An object may have a chage ±e, o ± e, o ± 3e, etc. but not ±1.5e. Poton has a chage 1e. lecton has a chage 1e. Some paticles such a neuton have no (zeo) chage. A neutal atom has as many positive and negative chages. Units In SI, electical chage is measued in coulomb ( ). The value of e = x Insulatos and onductos Mateial classification Miniquiz: Mateials/substances may be classified accoding to thei capacity to cay o conduct electic chage onductos ae mateial in which electic chages move feely. Insulato ae mateials in which electical chage do not move feely. Glass, Rubbe ae good insulatos. oppe, aluminum, and silve ae good conductos. Semiconductos ae a thid class of mateials with electical popeties somewhee between those of insulatos and conductos. Silicon and gemanium ae semiconductos used widely in the fabication of electonic devices. Identify substances o mateials that can be classified as onductos? Insulatos? 7 8

3 15. Insulatos and onductos haging by onduction. onside negatively chage ubbe od bought into contact with a neutal conducting but insulated sphee. Some electons located on the ubbe move to the sphee. Remove the ubbe od. xcess electons left on the sphee. It is negatively chaged. This pocess is efeed as chaging by conduction. 15. Insulatos and onductos ath/gound. When a conducto is connected to ath with a conducting wie o pipe, it is said to be gounded. ath povides a quasi infinite esevoi of electons: can accept o supply an unlimited numbe of electons Insulatos and onductos haging by Induction. onside a negatively chaged ubbe od bought nea a neutal conducting sphee insulated fom the gound. Repulsive foce between electons causes edistibution of chages on the sphee. lectons move away fom the od leaving an excess of positive chages nea the od. onnect a wie between sphee and ath on the fa side of the sphee. Repulsion between electons cause electons to move fom sphee to ath. Disconnect the wie. The sphee now has a positive net chage. This pocess is efeed as chaging by induction. haging by induction equies no contact with the object inducing the chage Insulatos and onductos haging by Induction. onside a negatively chaged ubbe od bought nea a neutal conducting sphee insulated fom the gound. Repulsive foce between electons causes edistibution of chages on the sphee. lectons move away fom the od leaving an excess of positive chages nea the od. onnect a wie between sphee and ath on the fa side of the sphee. Repulsion between electons cause electons to move fom sphee to ath. Disconnect the wie. The sphee now has a positive net chage. This pocess is efeed as chaging by induction. haging by induction equies no contact with the object inducing the chage. Q: How does this mechanism wok if we use a positively chaged glass od instead? 1 3

4 15. Insulatos and onductos Polaization. Polaization is ealignment of chage within individual molecules. Poduces induced chage on the suface of insulatos. how e.g. ubbe o glass can be used to supply electons. Miniquiz A positively chaged object hanging fom a sting is bought nea a non conducting object (ball). The ball is seen to be attacted to the e object. 1.xplain why it is not possible to detemine whethe the object is i negatively chaged o neutal..what additional expeiment is needed to eveal the electical chage state of the object?? xplain why it is not possible to detemine whethe the object is negatively chaged o neutal. What additional expeiment is needed to eveal the electical chage state of the object? Two possibilities: Attaction between objects of unlike chages. Two xpeiments: Bing a known neutal ball nea the object and obseve whethe thee is an attaction.? 0 Attaction between a chaged object and a neutal object subject to polaization. Bing a known negatively chage object nea the fist one. If thee is an attaction, the object is neutal, and the attaction is achieved by polaization

5 15.3 oulomb s s Law Obsevation hales oulomb discoveed in 1785 the fundamental law of electical foce between two stationay chaged paticles. An electic foce has the following popeties: Invesely popotional to the squae of the sepaation,,, between the paticles, and is along a line joining them. Popotional to the poduct of the magnitudes of the chages q 1 and q on the two paticles. Attactive if the chages ae of opposite sign and epulsive if the chages have the same sign. q 1 q 15.3 oulomb s s Law Mathematical Fomulation q1 q F = ke k e known as the oulomb constant. Value of k e depends on the choice of units. SI units Foce: the Newton (N) hage: the coulomb ( ). uent: the ampee (A =1 /s). Distance: the mete (m). xpeimentally measuement: k e = Nm /. Reasonable appoximate value: k e = Nm / xample hage and Mass of the lecton, Poton and Neuton. Paticle lecton Poton Neuton hage ( ) Mass (kg) e = c Takes 1/e= potons to ceate a total chage of 1 Numbe of fee electons in 1 cm 3 coppe ~ 10 3 hage obtained in typical electostatic expeiments with ubbe o glass 10 6 = 1 μc A vey small faction of the total available chage

6 15.3 oulomb s s Law Remaks The electostatic foce is often called oulomb foce. It is a foce (thus, a vecto): a magnitude a diection. F 1 q 1 q F 1 q 1 F 1 F 1 q MiniQuiz Name the fist action at a distance foce you have encounteed in physics so fa. Second example of action at a distance. 1 xample: lectical Foce The electon and poton of a hydogen atom ae sepaated (on the aveage) by a distance of about 5.3x10 11 m. Find the magnitude of the electic foce that each paticle exets on the othe. The electon and poton of a hydogen atom ae sepaated (on the aveage) by a distance of about 5.3x10 11 m. Find the magnitude of the electic foce that each paticle exets on the othe. Obsevations: We ae inteested in finding the magnitude of the foce between two paticles of known chage, and a given distance of each othe. The magnitude is given by oulomb s s law. q 1 =1.60x10 19 q =1.60x10 19 = 5.3x10 11 m F = k e q q

7 The electon and poton of a hydogen atom ae sepaated (on the aveage) by a distance of about 5.3x10 11 m. Find the magnitude of the electic foce that each paticle exets on the othe. Obsevations: We ae inteested in finding the magnitude of the foce between two paticles of known chage, and a given distance of each othe. The magnitude is given by oulomb s s law. q 1 =1.60x10 19 q =1.60x10 19 = 5.3x10 11 m Solution: 19 e 9 ( ) Nm 8 Fe = ke = = N m ( ) Attactive foce with a magnitude of 8.x10 8 N. Supeposition Pinciple Fom obsevations: one finds that wheneve multiple chages ae pesent, the net foce on a given chage is the vecto sum of all foces exeted by othe chages. lectic foce obeys a supeposition pinciple. 5 6 xample: Using the Supeposition Pinciple onside thee point chages at the cones of a tiangle, as shown below. Find the esultant foce on q 3 if q 1 = 6.00 x 10 9 q =.00 x 10 9 q 3 = 5.00 x 10 9 onside thee point chages at the cones of a tiangle, as shown below. Find the esultant foce on q 3. y q 3.00 m F 31 F m 37.0 o q 3 y q 1 x q 3.00 m q 1 F 31 F m 37.0 o q 3 x Obsevations: The supeposition pinciple tells us that the net foce on q 3 is the vecto sum of the foces F 3 and F 31. The magnitude of the foces F 3 and F 31 can calculated using oulomb s law

8 onside thee point chages at the cones of a tiangle, as shown below. Find the esultant foce on q 3. Solution: q 3.00 m q 1 y F 31 F 4.00 m o 5.00 m x o 9 Fx = F3 F31 cos37.0 = N o 9 Fy = F31 sin 37.0 = N 9 F = Fx Fy = ( )( ) q3 q 9 Nm 9 F3 = ke = = N ( 4.00m) 9 9 ( )( ) q3 q1 9 Nm 8 F31 = ke = = N θ = 65. o N q 3 ( 5.00m) Lightning Review 1. Popeties of electic chage two types: positive and negative always conseved and quantized. Insulatos and conductos chages move feely in conductos; opposite is tue fo insulatos conductos can be chaged by conduction and induction; insulatos can be polaized Review Poblem: Opeatingoom oom pesonnel must wea special conducting shoes while woking aound oxygen. Why? What might happen if pesonnel woe odinay ubbe shoes (sneakes)? 9 30 xample: Fun with units 15.4 lectic Field Discovey F = k e Recall that units can be manipulated: q q 1 [ ] [ ] [ q ][ ] 1 q F = ke [ ] [ ] [ ] [ oulomb ][ oulomb ] Newton = k e [ mete] lectic foces act though space even in the absence of physical contact. Suggests the notion of electical field (fist intoduced by Michael Faaday ( ). 1867). An electic field is said to exist in a egion of space suounding a chaged object. If anothe chaged object entes a egion whee an electical field is pesent, it will be subject to an electical foce. [ k ] e = N m

9 15.4 lectic Field Quantitative Definition 15.4 lectic Field Quantitative Definition () A field : geneally changes with position (location) A vecto quantity : magnitude and diection. Magnitude at a given location xpessed as a function of the foce impated by the field on a given test chage. Diection defined as the diection of the electical foce exeted on a small positive chage placed at that location. = F q o lectic Field lectic Field of a hage q If q>0, field at a given point is adially outwad fom q. Given F = k e qq o q q o One finds = q ke If q<0, field at a given point is adially inwad fom q. q q o

10 PoblemSolving Stategy lectic Foces and Fields Units: Fo calculations that use the oulomb constant, k e, chages must be in coulombs, and distances in metes. onvesion ae equied if quantities ae povided in othe units. Applying oulomb s s law to point chages. It is impotant to use the supeposition pinciple popely. Detemine the individual foces fist. Detemine the vecto sum. Detemine the magnitude and/o the diection as needed. xample: An electon moving hoizontally passes between two hoizontal planes, the uppe plane chaged negatively, and the lowe positively. A unifom, upwaddiected diected electic field exists in this egion. This field exets a foce on the electon. Descibe the motion of the electon in this egion. v o v o v o Obsevations: Hoizontally: No electic field No foce No acceleation onstant hoizontal velocity F a v x x x x = 0 = 0 = 0 = v o o x = vt Obsevations: Vetically: onstant electic field onstant foce onstant acceleation Vetical velocity incease linealy with time. F y o y o o a = q / m v = = q y o o o = q t/ m y o o o 1 y = q t / m o o o

11 xample: lectic Field Due to Two Point hages hage q 1 =7.00 μ is at the oigin, and chage q =10.00 μ is on the x axis, m fom the oigin. Find the electic field at point P, which has coodinates (0,0.400) m. y onclusions: The chage will follow a paabolic path downwad. Motion simila to motion unde gavitational field only except the t downwad acceleation is now lage. 1 P m q m q x 41 4 hage q 1 =7.00 μ is at the oigin, and chage q =10.00 μ is on the x axis, m fom the oigin. Find the electic field at point P, which has coodinates (0,0.400) m. Obsevations: Fist find the field at point P due to chage q 1 and q. Field 1 at P due to q 1 is vetically upwad. Field at due to q is diected towads q. The net field at point P is the vecto sum of 1 and. The magnitude is obtained with = q ke hage q 1 =7.00 μ is at the oigin, and chage q =10.00 μ is on the x axis, m fom the oigin. Find the electic field at point P, which has coodinates (0,0.400) m. Solution: 6 q ( ) Nm 5 1 = ke = = N / 1 ( 0.400m) 6 q 9 ( ) Nm 5 = ke = = N / ( 0.500m) 3 5 x = 5 = N / 4 5 = sinθ = = N / y x y.4 10 / o y x = = N φ = actan( / ) =

12 15.5 lectic Field Lines A convenient way to visualize field pattens is to daw lines in the diection of the electic field. Such lines ae called field lines. Remaks: 1. lectic field vecto,, is tangent to the electic field lines at each point in space.. The numbe of lines pe unit aea though a suface pependicula to the lines is popotional to the stength of the electic field in a given egion lectic Field Lines () lectic field lines of single positive (a) and (b) negative chages. a) q b) q is lage when the field lines ae close togethe and small when fa apat lectic Field Lines (3) 15.5 lectic Field Lines (4) Rules fo dawing electic field lines fo any chage distibution. 1. Lines must begin on positive chages (o at infinity) and must teminate on negative chages o in the case of excess chage at infinity.. The numbe of lines dawn leaving a positive chage o appoaching a negative chage is popotional to the magnitude of the chage. 3. No two field lines can coss each othe. lectic field lines of a dipole

13 Application: Measuement of the atmospheic electic field The electic field nea the suface of the ath is about 100 N/ downwad. Unde a thundecloud, the electic field can be as lage as 0000 N/. How can such a (lage) field be measued? A A onductos in lectostatic quilibium Good conductos (e.g. coppe, gold) contain chages (electon) that ae not bound to a paticula atom, and ae fee to move within the mateial. When no net motion of these electons occu the conducto is said to be in electostatic equilibium onductos in lectostatic quilibium Popeties of an isolated conducto (insulated fom the gound). 1. lectic field is zeo eveywhee within the conducto.. Any excess chage field on an isolated conducto esides entiely on its suface. 3. The electic field just outside a chaged conducto is pependicula to the conducto s s suface. 4. On an iegula shaped conducto, the chage tends to accumulate at locations whee the adius of cuvatue of the suface is smallest at shap points

14 1. lectic field is zeo eveywhee within the conducto. If this was not tue,, the field inside would be finite. Fee chage thee would move unde the influence of the field. A cuent would be induced. The conducto would not be in an electostatic state.. Any excess chage field on an isolated conducto esides entiely on its suface. This popety is a diect esult of the 1/ epulsion between like chages. If an excess of chage is placed within the volume, the epulsive foce pushes them as fa apat as they can go. They thus migate to the suface The electic field just outside a chaged conducto is pependicula to the conducto s s suface. 4. On an iegula shaped conducto, the chage tends to accumulate at locations whee the adius of cuvatue of the suface is smallest st at shap points. If not tue, the field would have components paallel to the suface of the conducto. This field component would cause fee chages of the conducto to move. A cuent would be ceated. Thee would no longe be a electostatic equilibium. onside, fo instance, a conducto faily flat at one end and elatively pointed at the othe. xcess of chage move to the suface. Foces between chages on the flat suface, tend to be paallel to the suface. Those chages move apat until epulsion fom othe chages ceates an equilibium. At the shap ends, the foces ae pedominantly diected away fom the suface. Thee is less of tendency fo chages located at shap edges to move away fom one anothe. Poduces lage fields (and foce) nea shap edges

15 Remaks Faaday s s icepail expeiment Popety 4 is the basis fo the use of lightning ods nea houses and buildings. (Vey impotant application) Most of any chage on the house will pass though the shap point of the lightning od. Fist developed by B. Fanklin. Demonstates that the chage esides on the suface of a conducto Miniquiz Suppose a point chage Q is in empty space. Weaing ubbe gloves, we sneak up and suound the chage with a spheical conducting shell. What effect does this have on the field lines of the chage? Suppose a point chage Q is in empty space. Weaing ubbe gloves, we sneak up and suound the chage with a spheical conducting shell. What effect does this have on the field lines of the chage? Answe: Negative chage will build up on the inside of the shell. Positive chage will build up on the outside of the shell. Thee will be no field lines inside the conducto but the field lines will emain outside the shell. q? q

16 MiniQuiz Is it safe to stay inside an automobile duing a lightning stom? Why? Is it safe to stay inside an automobile duing a lightning stom?? Why? Answe: Yes. It is. The metal body of the ca caies the excess chages on its extenal suface. Occupants touching the inne suface ae in no dange. SAF