1 Lecture 1 Electric Charge Structure of Matter

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

Electric charge - experiments 2 Plexiglass Repulsion Plastic Attraction

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

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

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

Electric charge properties 7 Like charges repel; opposite charges attract. Charge is discrete (quantized) - The smallest charge possible is = 1. 602 x 10 -19 C (Coulombs) - Any charge is a integer multiple of the elementary unit of charge Charge is conserved - charge can be exchanged between different parts of a closed system, but the total charge of the system cannot change

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. 2. 3. 4. 5. 1 and 3 carry charges of opposite sign. 1 and 3 carry charges of equal size. all three carry charges of the same sign. one of the objects carries no charge. we need to do more experiments

Types of materials 9 Conductors - charges move freely (Ex. metals). One consequence of this property is that the charge that is transferred to a spread do outnot uniformly on its(Ex. surface. conductor Insulatorswill - charges move freely 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)

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

Charging mechanisms 11 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)

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

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

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 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. 2. 3. 4. A B C D ++++ + + A - -+ + + -+ B C ++ + +- D

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. 2. 3. 4. A B C D

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.

Solution 18 - 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 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. 2. 3. 4. 5. 1 and 3 carry charges of opposite sign. 1 and 3 carry charges of the same sign. all three carry charges of the same sign. one of the objects carries no charge. we need to do more experiments

Coulomb's Law Explored by Charles Augustin de Coulomb 20

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

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? 1. 2. 3. 4. 5. 6. 1 2 3 4 5 6 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

23 Which graph best represents the magnitude of the interaction force between two positively charged ions as a function of the distance separating them? 1. 2. 3. 4. B A A B C D D C 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

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 (~ 1035 times stronger)

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 1039 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? 1. 2. 3. Yes, we must move the particles further apart. Yes, we must move the particles closer, together. No, at any distance. 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Superposition principle 26 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?

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

28 Example 2: - Planar distribution (vector nature of Coulomb's law) Find the magnitude and direction of the force on Q. 1 1 3 2

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

30 Problem Two free point charges +q and +4 q 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. L +q +4 q Extra credit (5 points) – due Wednesday, September 7

Review – dealing with vector summation Question: How do we express the sum vector parameters (F, q), if we know them for the individual vectors, i. e. (F 1, q 1) and (F 2, q 2). 31 y F 1 x F 2 x x F 2 y For the sum vector: - the q angles are always measured clockwise towards the positive x axis y Fy Fx x

32 Extracredit Problem – Assigned on 09/03/2010 Two free point charges +q and +4 q 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 qo 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 Step 2: - determine the condition for the charge q or 4 q to be at equilibrium.

Problem (Chapter 21, Problem 4 – Page 574) 34 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? 1 q q/2 2 q q 3 q/4 3 0 q/2 3 q/4 F 12 F F/2 3 F/8

35 In the following diagram what is the direction of the electrostatic force on the negative charge -q? Q 1. 2. -q 3. 4. 5. none of the above Q 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

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. 2. 3. 4. 5. F/16 F/8 F/4 F/2 F 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Electric Field 38 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

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

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

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. 41 Positive charge q 0 placed in an electric field - Negative charge q 0 placed in an electric field

Electric field due to a point charge 42