PHYSICS 632 SUMMER :00 10:50 Room 203 Electricity, Magnetism and Light. Richard A. Lindgren, Office Room 302

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2 PHYSICS 632 SUMMER :00 10:50 Room 203 Electricity, Magnetism and Light Richard A. Lindgren, Office Room 302 Text: Halliday, Resnick, and Walker, 7 th edition, Extended Version, Starting with Chapter 21 on Charge. 2

3 Your Goals and Interest get a degree crossover teaching fill in knowledge gaps review, learn new teaching ideas peer learning modeling inquiry learning group learning new experiments and demos computer technology solidify concepts learn how to do problems. 3

4 Assignments See syllabus for daily homework assignments using WebAssign. Work on problems in recitation after lecture. Discuss with TA s and others in the apartments at night. Due at 8:00 am next day. Algebra, trigonometry, unit vectors and vectors, derivatives and integration review. How do you improve problem-solving skills. Lots of practice and more practice. Quizzes on second three Tuesdays and final on WebAssign, 30% conceptual questions, 70% problem oriented. There will also be 4 homework assignments due in August and September. Final exam at the end of September on WebAssign. 4

5 Class Organization Cartoon Demonstrations Lecture and discussion Experiments and demos with explanations Hand-worked problems on Elmo Clicker/Polling problems 5

6 References and other Texts Calculus-Based Physics II (download) Schnick ml Physics for Scientists and Engineers, 6 th Edition Serway, Jewett Physics for Scientists and Engineers, 3 rd Edition Fishbane, Gasiorowicz, Thornton Physics for Scientists & Engineers, 4 th Edition Giancoli Principals of Electricity Page, Adams 6

7 Lecture 1 Charge Ch. 21 Electrostatics: study of electricity when the charges are not in motion. Good place to start studying E&M because there are lots of demonstrations. Cartoon - Charge is analogous to mass Demo - Large Van de Graaff Math Review and Tooling up Topics What is electric charge? Point objects, Size. Atomic model Methods of charging objects. Friction,Contact, Induction, Machines Instruments to measure charge Quantization of charge and conservation of charge Coulombs Law and examples Principle of superposition and examples Demos Elmo Two pennies Three charges in a plane Hanging path ball Polling 7

8 Charged Hair Van de Graaff Demo Need a female teacher to come forward. How does this gadget produce a mini-lightning bolt? What upward forces are keeping your hair up? How are these forces produced? Why do the hair strands spread out from each other? Why do they spread out radially from the head? Is hair a conductor or insulator? How can we find out? Does it depend if is wet or dry. To understand what is going on we need to know about charge and we need a model of electricity. 8

9 In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself more valuable than 20 formulae. Albert Einstein 9

10 Charge What is charge? How do we visualize it. We only know charge exists because in experiments electric forces cause objects to move. Charge is analogous to mass in mechanics. We know how it behaves, but we don t know what it really is. The same is true for charge.. Need more experiments to get the point across. UVa Electrostatics Kit ( Rub a Balloon 2 x 4 on glass. Need a model 10

11 More on charging using the UVa Electrostatic Kit 11

12 Bohr Model 12

13 3 protons, 3 neutrons 13

14 More complicated than just protons, neutrons, and electrons, but this will suffice. Electron: Considered a point object with radius less than meters with electric charge e= -1.6 x Coulombs (SI units) and mass m e = 9.11 x kg Proton: It has a finite size with charge e, mass m p = 1.67 x kg and with radius / x m scattering experiment / x m Lamb shift experiment Neutron: Similar size as proton, but with total charge = 0 and mass m n = Positive and negative charges exists inside the neutron Pions: Smaller than proton. Three types: e, - e, 0 charge and radius 0.66 / x m Quarks: Point objects. Confined to the proton and neutron, Not free Proton (uud) charge = 2/3e 2/3e -1/3e = e Neutron (udd) charge = 2/3e -1/3e -1/3e = 0 An isolated quark has never been found 14

15 Normally atoms are in the lowest energy state. This means that the material is electrically neutral. You have the same number of electrons as protons in the material. How do we change this? How do we add more electrons than protons or remove electrons? There are several different ways. 15

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17 More on our Model of electricity Consider solid material like a piece of copper wire. The proton core is fixed in position in a lattice like structure. In a conductor, the valence electrons are free to move about. How many electrons are free to move about? 1cm long and a radius of 0,005 cm Copper (Face Centered Cube) - good conductor Copper atom: Z=29(protons), N= 34(neutrons), 29 Electrons Carbon or diamond - poor conductor 17

18 Summary Comments Silk() on teflon(-) Silk (-) on acrylic () Wood doesn t charge Charged objects always attract neutral objects Show Triboelectric series Not only chemical composition important, structure of surface is important - monolayer of molecules involved, quantum effect. (nanotechnology) 18

19 Triboelectric series Positive (Lose electrons easily) Air Human Hands Asbestos Rabbit Fur Glass Mica Acrylic Human Hair Nylon Wool Fur Lead Silk Aluminum Paper Cotton Steel Wood Amber Sealing Wax Hard Rubber Nickel, Copper Brass, Silver Gold, Platinum Sulfur Acetate, Rayon Polyester Styrene Orlon Saran Balloon Polyurethane Polypropylene Vinyl (PVC) Silicon Teflon Negative (Gains electrons easily) 19

20 Electrostatics is based on 4 four empirical facts Conservation of charge Quantization of charge Coulombs Law The principle of superposition 20

21 Conservation of charge Rubbing does not create charge, it is transferred from object to another Teflon negative - silk positive Acrylic positive - silk negative Demo: Show electronic electroscope with cage: gives magnitude and sign of charge. Use teflon and silk to show and -. Nuclear reactions γ 0 = e e - Radioactive decay 238 U 92 = 234 Th 90 4 He 2 High energy particle reactions e - p = e - π n 0 21

22 What is meant by quantization of charge? Discovered in 1911 by Robert A. Millikan in the oil drop experiment The unit of charge is so tiny that we will never notice it comes in indivisible lumps. Example: Suppose in a typical experiment we charge an object up with a nanocoulomb of charge (Q = 10-9 C). How many elementary units, N, of charge is this? Elementary unit of charge e = "19 C N = Q e = 10 9 C 1.6 " C = " 1010 = 6.25 " 10 9 Six billion units of charge 22

23 Coulombs Law Lab Experiment In 1785 Charles Augustin Coulomb reported in the Royal Academy Memoires using a torsion balance two charged mulberry pithballs repelled each other with a force that is inversely proportional to the distance. F=k q 1 q 2 r 2 where k = Nm 2 /C 2 Also F= 1 4" 0 q 1 q 2 r 2 where " 0 = 8.85 # C 2 / N. m 2 F=G m 1 m 2 r 2 Electrical Permittivity of vacuum q 1 r q 2 Repulsion Point charges - Spheres same as points - - Attraction Repulsion 23

24 Coulombs Law Two Positive Charges What is the magnitude of the force between two positive charges, each 1 nanocoulomb, and 1cm apart in a typical demo? q 1 r q 2 1 nc 1 cm 1 nc F= kq 1q 2 r 2 ( ) 10 "9 c F = Nm C 2 ( ) 2 = 9 10 ( 10 "2 m) "5 N 2 What is the direction of the force? (Equivalent to the weight of a long strand of hair) 1 nc 1 cm Repulsion 1 nc What is the direction of the force in unit vector notation? 24

25 What is the direction of the force in unit vector notation? 1 nc 1 cm 1 nc 1 2 y ĵ î x F 1 = 9 " 10 5 N î F 2 = 9 10 "5 N î ( ) 10 "9 c F = Nm C 2 ( ) 2 = 9 10 ( 10 "2 m) "5 N 2 25

26 Coulombs Law in vector notation. F 12 = k q 1 q 2 r 2 ˆr 12 F 12. q 1. q 2 ˆr 12 where: F is the force exerted by particle 1 on particle 2, 12 ˆr 12 is a unit vector in the direction from 1 to 2, and k, q 1, and q 2 are defined as before (the Coulomb constant, the charge on particle 1, and the charge on particle 2 respectively). ( ) 10 "9 c F 12 = Nm C 2 ( )( 10 "9 c) ˆr ( 10 "2 m) 2 12 = 9 10 "5 N ˆr 12 The positive sign means the force on q 2 is in the same direction as the unit vector r 26

27 How do you write the Force on q 1 F 21 = k q 1 q 2 r 2 ˆr 21 ˆr 21.q 1. q 2 F 21 where: F 21 is the force exerted by particle 2 on particle 1, ˆr 21 is a unit vector in the direction from 2 to 1, and k, q 1, and q 2 are defined as before (the Coulomb constant, the charge on particle 1, and the charge on particle 2 respectively). ( ) 10 "9 c F 21 = Nm C 2 ( )( 10 "9 c) ˆr ( 10 "2 m) 2 12 = 9 10 "5 N ˆr 21 The positive sign means the force on q 1 is in the same direction as the unit vector. r 27

28 Principle of Superposition Three charges In a line Example Three charges lie on the x axis: q 1 =25 nc at the origin, q 2 = -12 nc at x = 2m, q 3 =18 nc at x=3 m. What is the net force on q 1 and the direction of the force? We simply add the two forces keeping track of their directions. 1 2 ˆr 21 ˆr 31 F net,1 = F 21 F 31 F net,1 = k q q 1 2 ˆr 2 21 k q q 1 3 q ˆr 2 31 = kq 2 1 ˆr 2 21 q $ 3 ˆr 2 31 r 21 r 31 " # r 21 r 31 % & # "12 10 = ( "9 C Nm2 C )(25 10 "9 C) ˆr 2 (2m) "9 C & ˆr (3m) 2 31 $ % ' ( = ( Nm2 C )(25 10 "9 C) ("3 10 "9 C ˆr "9 C ˆr 31 ) = 2.25 " 10 7 N ˆr 21 (Directed in the positive x direction) 3 x 28

29 Uniformly charged metal spheres of Radius R F= kq2 (r) 2 F kq2 (r2r) 2 Demo: Show uniformity of charge around sphere using electrometer. Demo: Show charging spheres by induction using electrometer 29

30 Coulombs Law (Use Elmo) Two Pennies without electrons What is the force between two 3 gm pennies one meter apart if we remove all the electrons from the copper atoms? 30

31 What is the force on charge q 1 due to many other charges lying in a plane. I would like to show you another notation. F net = F 12 F 13 F 12 = kq 1q 2 (r 12 ) 2 ˆr 12 F net = N i=2 F 1i r 13 -q 3 F 13 = kq 1 q 3 (r 13 ) 2 ˆr 13 ˆr 13 ˆr 12 q 1 r 12 q 2 F 12 F net q 1 F 13 -q 3 q 2 In practice you find the x and y comonents of all the vectors and add them 31 up F 13 F 12 F net

32 Example: Three point charges in a plane q 3 = - 2 nc (Use Elmo) y 5 cm 2 cm q 1 = 1 nc 1 cm x q 2 = 1 nc Question: What is the net force on q 1 and in what direction? Hint : Find x and y components of force on q 1 due to q 2 and q 3 and add them up. 32

33 In an atom can we neglect the gravitational force between the electrons and protons? What is the ratio of Coulomb s electric force to Newton s gravity force for 2 electrons separated by a distance r? q r F c = kee r 2 F c F g = ke2 Gm 2 q m r F g = Gmm r 2 m F c F g = ( ) 2 ( ) 2 ( Nm 2 ) "19 C C 2 ( "11 Nm 2 ) "31 kg kg 2 = Huge number - pure number - no units 33

34 Why are neutral objects always attracted to positive or negative charged objects. For example: Rubbed balloon is attracted to wall Comb is attracted to small bits of paper Clothes in the dryer stick together. Demo: Put wood on the spinner and place charged teflon and plastic rods near it. What is the explanation of all of these phenomena? 34

35 Explanation: The neutral objects atoms and molecules orient themselves in the following way so that the Coulomb forces due to attraction are greater than those due to repulsion because the latter are further away. (Inverse square Law) Acrylic Rod Wooden block F = kq1q 2 r 2 Acrylic Rod Attraction Wooden block Repulsion Attractive forces >> Repulsive Forces 35

36 Show induction: Click on 08/lecture_1.html -- Demo: Using conducting spheres and electrometer Demo: Electrophorus Demo: Electroscope Demo: hanging charged/conducting pith ball- first attraction by induction, then contact, then conduction of charge, then repulsion Problem: Two equally charged hanging pith balls (Use Elmo) 36

37 Chapter 21 Problem 29 In crystals of a certain salt, singly charged cations form the eight corners of a cube and a singly charged anion is at the cube's center (Figure 21-32). The edge length of the cube is x = 0.32 nm. The cations are each deficient by one electron (and thus each has a charge of e), and the anion has one excess electron (and thus has a charge of -e). Fig (a) What is the magnitude of the net electrostatic force exerted on the anion by the eight cations at the corners of the cube? (b) If one of the cations is missing, the crystal is said to have a defect. What is the magnitude of the net electrostatic force exerted on the 37 anion by the seven remaining cations?

38 Chapter 21 Problem 68 Figure In Figure particles 1 and 2 are fixed in place, but particle 3 is free to move. If the net electrostatic force on particle 3 due to particles 1 and 2 is zero and L 23 =2.00 L 12, what is the ratio q 1 /q 2? 38