1. 1 Lecture 1  Electric Charge  Structure of Matter 08/30/2010  Conductors and Insulators  Charging Mechanisms  Coulomb’s law  Superposition principle

2. 2 Electric charge - experiments RepulsionAttraction Plexiglass Plastic

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4. 4 PlexiglassPlastic PlexiglassRepelsAttracts PlasticAttractsRepels electric charge New physical property of matter: electric charge Electric charge electrical forces Charged bodies interact through: electrical forces Need two flavors to explain the existence of repulsive as well as attractive forces positive (+) and negative (-)

5. 5 Microscopic view of matter Elementary particles: Number of electrons = Number of protons The atom is neutral

6. 6 Electric charges Like charges repel; opposite charges attract. Examples of charges: electrons (negative); protons (positive) Two types of charges: positive (+) and negative (-) Type of materials: insulators, conductors (Ex metals), semiconductors

7. 7 Electric charge properties Like charges repel; opposite charges attract. Charge is discrete (quantized) - The smallest charge possible is = - Any charge is a integer multiple of the elementary unit of charge 1.602 x 10 -19 C (Coulombs) Charge is conserved - charge can be exchanged between different parts of a closed system, but the total charge of the system cannot change

8. 8 Three pithballs are suspended from thin threads. It is found that pithballs 1 and 2 repel each other and that pithballs 2 and 3 repel each other. From this we can conclude that: 1. 1 and 3 carry charges of opposite sign. 2. 1 and 3 carry charges of equal size. 3. all three carry charges of the same sign. 4. one of the objects carries no charge. 5. we need to do more experiments

9. 9 Types of materials Conductors - charges move freely (Ex. metals). One consequence of this property is that the charge that is transferred to a conductor will spread out uniformly on its surface. Insulators - charges do not move freely (Ex. glass, plastic). Semiconductors - intermediate case - charges can move freely under in some special cases (higher temperature, applied voltage) (silicon, germanium). Superconductors – extremely good conductors = zero resistance. Restricted to very low temperatures. (Ex. niobium, BISCO)

10. 10 Electroscope and Van de Graaff generator Electroscope: used to measured charge by measuring the deflection of charged metal foils Van de Graaff generator. 

11. 11 Charging mechanisms Objects can become charged when elementary charged particles (most probably electrons) are transferred from one object to the other. - When a glass rod and fur are rubbed together some electrons are transferred to the fur (triboelectricity)

12. 12 Charging by contact - Electrons are transferred from the plastic rod to the metal ball

13. 13 When a neutral metal sphere is charged by contact with a positively charged glass rod, the sphere: 1. loses electrons 2. gains electrons 3. loses protons 4. gains protons

14. 14 Charging by induction - The copper rod is attracted to the charged glass rod even if initially is uncharged and does not contact the glass rod at any time.

15. 15 The diagram below shows a neutral metal sphere on a isolating pedestal. Which of the other diagrams shown, describes best the charge distribution on the sphere when a negatively charged rod is brought in its vicinity? 1. A 2. B 3. C 4. D A B C D + + + + - - - - + + + + + + + + + -+ + - - - + +

16. 16 The diagram below shows three identical neutral metal spheres on a isolating pedestals, which are in contact. Which of the other diagrams shown, describes best the charge distribution on the spheres when a negatively charged rod is brought in its vicinity? 1. A 2. B 3. C 4. D AB C D

17. 17 A negatively charged plastic rod is brought in the vicinity of a neutral metal ball placed on a isolating pedestal. If the opposite side of the sphere is briefly connected to the ground and then the plastic rod is removed, what will the final charge on the ball be? 1.The metal ball will be neutral as initially. 2.The metal ball will be positively charged 3.The metal ball will be negatively charged.

18. 18 Solution - Due to the interaction with the plastic rod, positive and negative charges will be separated on the ball. Through the grounding loop the electrons are transferred to the Earth which acts as an infinite sink or source of electrons, leaving the sphere with a deficit of electrons (positively charged)

19. 19 Three metal balls are suspended from thin threads. It is found that balls 1 and 2 attract each other and that balls 2 and 3 repel each other. From this we can definitely conclude that: 1. 1 and 3 carry charges of opposite sign. 2. 1 and 3 carry charges of the same sign. 3. all three carry charges of the same sign. 4. one of the objects carries no charge. 5. we need to do more experiments

20. 20 Coulomb's Law Explored by Charles Augustin de Coulomb

21. 21 Coulomb's law properties Inverse square law Direction: along the line joining the charges Attractive for unlike charges and repulsive for like charges Newton’s 3 rd Law action reaction pair:

22. 22 Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces? 20 1. 1 2. 2 3. 3 4. 4 5. 5 6. 6 1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950

23. 23 Which graph best represents the magnitude of the interaction force between two positively charged ions as a function of the distance separating them? 20 A B C D 1. A 2. B 3. C 4. D 1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950

24. 24 Coulomb's law vs. Newton law of gravitation Inverse square laws - force acting along the line joining the particles.  There are two kinds of charges, but only one type of mass. Gravity is always attractive. The electrostatic force, (e.g., between an electron and proton), is enormously stronger (~ 10 35 times stronger)

25. 25 A hydrogen atom is composed of a nucleus containing a single proton, about which a single electron orbits. The electric force between the two particles is 2.3 x 10 39 greater than the gravitational force! If we can adjust the distance between the two particles, can we find a separation at which the electric and gravitational forces are equal? 20 1. Yes, we must move the particles further apart. 2. Yes, we must move the particles closer, together. 3. No, at any distance. 1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950

26. 26 Superposition principle When two or more charges each exert a force on a charge, the total force on that charge is the vector sum of the forces exerted by the individual charges. Example: - Linear distribution What is the net force acting on q 3 ?

27. 27 Solution: Step 1 : - Calculate the force produce by each charge Step 2 : - Add all the forces using vector summation rules

28. 28 Example 2: - Planar distribution (vector nature of Coulomb's law) Find the magnitude and direction of the force on Q.    

29. 29 Step 1 : - find the force exerted by each charge on Q The components on the x and y axis of are: with Step 2 : - Add the two forces (addition using components) Obtain the F 2onQ components in a similar way

30. 30 +q+4q L Extra credit (5 points) – due Wednesday, September 7 Problem Two free point charges +q and +4q are located a distance L, apart. A third charge is placed so that the whole system is in equilibrium. Find the location, magnitude, and sign of the third charge.

31. 31 Review – dealing with vector summation y x F 1x F 2x F 2y F 1y  the  angles are always measured clockwise towards the positive x axis x FxFx FyFy y For the sum vector  Question: How do we express the sum vector parameters (F,  ), if we know them for the individual vectors, i.e. (F 1,  1 ) and (F 2,   

32. 32 Extracredit Problem – Assigned on 09/03/2010 Two free point charges +q and +4q are located a distance L, apart. A third charge is placed so that the whole system is in equilibrium. Find the location, magnitude, and sign of the third charge. Solution: Step 1: - determine the condition for the charge q o to be at equilibrium. Call the new charge, q 0, and let it be distance x from +q. The free-body diagram shows relationship of the two forces on the new charge:

33. 33 Step 2: - determine the condition for the charge q or 4q to be at equilibrium.

34. 34 Problem (Chapter 21, Problem 4 – Page 574) Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Figure a). The electrostatic force acting on sphere 2 due to sphere 1 is F. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Figure b), then to sphere 2 (Figure c), and finally removed (Figure d). The electrostatic force that now acts on sphere 2 has magnitude F’. What is the ratio F’/F? 123F 12 qq0F q/2q F/2 q/23q/4 3F/8

35. 35 In the following diagram what is the direction of the electrostatic force on the negative charge -q? 1. 2. 3. 4. 5.none of the above Q Q - q 20 1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950

36. 36 In the figure a charged particle of charge (- q) is surrounded by two circular rings of charged particles. What is the net force on the central particle due to the other particles? 1. 2. 3. 4. 5. 20 1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950

37. 37 Two small charged objects attract each other with a force F when separated by a distance d. If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2 the force becomes: 1.F/16 2.F/8 3.F/4 4. F/2 5. F 20 1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950

38. 38 Electric Field Why do we need this concept? - Coulomb's law describes action at distance (like gravitation). - Any charge changes the properties of the space around it. - We need a field to describe this change. The notion of field is not a new one: - A field is a quantity that is assigned a value at each point in a region of space

39. 39 Vector field Wind speed - the absolute value and direction is known. © http://maps.wunderground.com/

40. 40 Back to the electric field - Units: N/C - E does not depend on the test charge q 0. Note: The rest of this chapter and chapter 23 are mostly dedicated to how to determine the magnitude and orientation of different electric. To calculate the electric field of a charge distribution use superposition 

41. 41 Force on a charge in an electric field The direction of the force acting on a point charge in an electric field depends on both the direction of the electric field and the sign of the charge. Positive charge q 0 placed in an electric field Negative charge q 0 placed in an electric field -

42. 42 Electric field due to a point charge