1. Lecture 10 Chapter 15 Chapter 16 Chapter 17 Chapter 18

2. Fig. 15-CO, p.497

3. First Observations – Greeks Observed electric and magnetic phenomena as early as 700 BC Found that amber, when rubbed, became electrified and attracted pieces of straw or feathers Also discovered magnetic forces by observing magnetite attracting iron

4. Fig. 15-1b, p.498

5. Fig. 15-2, p.499

6. Fig. 15-3a, p.499

7. Fig. 15-1, p.498

8. Properties of Charge, final Charge is quantized All charge is a multiple of a fundamental unit of charge, symbolized by e Quarks are the exception Electrons have a charge of –e Protons have a charge of +e The SI unit of charge is the Coulomb (C) e = 1.6 x 10 -19 C

9. Conductors Conductors are materials in which the electric charges move freely in response to an electric force Copper, aluminum and silver are good conductors When a conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material

10. Insulators Insulators are materials in which electric charges do not move freely Glass and rubber are examples of insulators When insulators are charged by rubbing, only the rubbed area becomes charged There is no tendency for the charge to move into other regions of the material

11. Semiconductors The characteristics of semiconductors are between those of insulators and conductors Silicon and germanium are examples of semiconductors

12. Charging by Conduction A charged object (the rod) is placed in contact with another object (the sphere) Some electrons on the rod can move to the sphere When the rod is removed, the sphere is left with a charge The object being charged is always left with a charge having the same sign as the object doing the charging

13. Fig. 15-5a, p.501

14. Fig. 15-5b, p.501

15. Coulomb’s Law Coulomb shows that an electrical force has the following properties: It is along the line joining the two particles and inversely proportional to the square of the separation distance, r, between them It is proportional to the product of the magnitudes of the charges, |q 1 |and |q 2 |on the two particles It is attractive if the charges are of opposite signs and repulsive if the charges have the same signs

16. Coulomb’s Law, cont. Mathematically, k e is called the Coulomb Constant k e = 8.9875 x 10 9 N m 2 /C 2 Typical charges can be in the µC range Remember, Coulombs must be used in the equation Remember that force is a vector quantity Applies only to point charges Coulomb's law Coulomb's law

17. Characteristics of Particles

18. Fig. 15-6a, p.502

19. Fig. 15-6b, p.502

20. Electrical Forces are Field Forces This is the second example of a field force Gravity was the first Remember, with a field force, the force is exerted by one object on another object even though there is no physical contact between them There are some important similarities and differences between electrical and gravitational forces

21. The Superposition Principle The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges that are present. Remember to add the forces as vectors

22. Fig. 15-8, p.504

23. Electrical Forces are Field Forces This is the second example of a field force Gravity was the first Remember, with a field force, the force is exerted by one object on another object even though there is no physical contact between them There are some important similarities and differences between electrical and gravitational forces

24. Electrical Force Compared to Gravitational Force Both are inverse square laws The mathematical form of both laws is the same Masses replaced by charges Electrical forces can be either attractive or repulsive Gravitational forces are always attractive Electrostatic force is stronger than the gravitational force

25. The Superposition Principle The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges that are present. Remember to add the forces as vectors

26. Fig. 15-8, p.504

27. Superposition Principle Example The force exerted by q 1 on q 3 is The force exerted by q 2 on q 3 is The total force exerted on q 3 is the vector sum of and

28. Fig. 15-9, p.505

29. Electric Field Mathematically, SI units are N / C Use this for the magnitude of the field The electric field is a vector quantity The direction of the field is defined to be the direction of the electric force that would be exerted on a small positive test charge placed at that point

30. Direction of Electric Field The electric field produced by a negative charge is directed toward the charge A positive test charge would be attracted to the negative source charge

31. Electric Field Lines A convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the field vector at any point These are called electric field lines and were introduced by Michael Faraday

32. Fig. 15-13a, p.510

33. Fig. 15-13b, p.510

34. Electric Field Line Patterns An electric dipole consists of two equal and opposite charges The high density of lines between the charges indicates the strong electric field in this region

35. Electric Field Line Patterns Two equal but like point charges At a great distance from the charges, the field would be approximately that of a single charge of 2q The bulging out of the field lines between the charges indicates the repulsion between the charges The low field lines between the charges indicates a weak field in this region

36. Electric Field Patterns Unequal and unlike charges Note that two lines leave the +2q charge for each line that terminates on -q

37. Fig. 15-18a, p.513

38. Fig. 15-18b, p.513

39. Van de Graaff Generator An electrostatic generator designed and built by Robert J. Van de Graaff in 1929 Charge is transferred to the dome by means of a rotating belt Eventually an electrostatic discharge takes place

40. Electrical Potential Energy of Two Charges V 1 is the electric potential due to q 1 at some point P The work required to bring q 2 from infinity to P without acceleration is q 2 V 1 This work is equal to the potential energy of the two particle system

41. The Electron Volt The electron volt (eV) is defined as the energy that an electron gains when accelerated through a potential difference of 1 V Electrons in normal atoms have energies of 10’s of eV Excited electrons have energies of 1000’s of eV High energy gamma rays have energies of millions of eV 1 eV = 1.6 x 10 -19 J

42. Equipotential Surfaces An equipotential surface is a surface on which all points are at the same potential No work is required to move a charge at a constant speed on an equipotential surface The electric field at every point on an equipotential surface is perpendicular to the surface

43. Equipotentials and Electric Fields Lines – Positive Charge The equipotentials for a point charge are a family of spheres centered on the point charge The field lines are perpendicular to the electric potential at all points

44. Equipotentials and Electric Fields Lines – Dipole Equipotential lines are shown in blue Electric field lines are shown in red The field lines are perpendicular to the equipotential lines at all points

45. Capacitance, cont Units: Farad (F) 1 F = 1 C / V A Farad is very large Often will see µF or pF

46. Parallel-Plate Capacitor The capacitance of a device depends on the geometric arrangement of the conductors For a parallel-plate capacitor whose plates are separated by air:

47. Parallel-Plate Capacitor, Example The capacitor consists of two parallel plates Each have area A They are separated by a distance d The plates carry equal and opposite charges When connected to the battery, charge is pulled off one plate and transferred to the other plate The transfer stops when V cap = V battery Demo 2

48. Capacitors in Parallel The total charge is equal to the sum of the charges on the capacitors Q total = Q 1 + Q 2 The potential difference across the capacitors is the same And each is equal to the voltage of the battery

49. Fig. 16-19, p.551

50. Fig. 16-20, p.552

51. Fig. P16-34, p.564

52. Fig. 16-21, p.553

53. Energy Stored in a Capacitor Energy stored = ½ Q ΔV From the definition of capacitance, this can be rewritten in different forms

54. Dielectric Strength For any given plate separation, there is a maximum electric field that can be produced in the dielectric before it breaks down and begins to conduct This maximum electric field is called the dielectric strength

55. Table 16-1, p.557

56. Electric Current Whenever electric charges of like signs move, an electric current is said to exist The current is the rate at which the charge flows through this surface Look at the charges flowing perpendicularly to a surface of area A The SI unit of current is Ampere (A) 1 A = 1 C/s

57. Electric Current, cont The direction of the current is the direction positive charge would flow This is known as conventional current direction In a common conductor, such as copper, the current is due to the motion of the negatively charged electrons It is common to refer to a moving charge as a mobile charge carrier A charge carrier can be positive or negative

58. Current and Drift Speed Charged particles move through a conductor of cross- sectional area A n is the number of charge carriers per unit volume n A Δx is the total number of charge carriers

59. Current and Drift Speed, cont The total charge is the number of carriers times the charge per carrier, q ΔQ = (n A Δx) q The drift speed, v d, is the speed at which the carriers move v d = Δx/ Δt Rewritten: ΔQ = (n A v d Δt) q Finally, current, I = ΔQ/Δt = nqv d A

60. Current and Drift Speed, final If the conductor is isolated, the electrons undergo random motion When an electric field is set up in the conductor, it creates an electric force on the electrons and hence a current

61. Charge Carrier Motion in a Conductor The zig-zag black line represents the motion of charge carrier in a conductor The net drift speed is small The sharp changes in direction are due to collisions The net motion of electrons is opposite the direction of the electric field DemoDemo

62. p.578

63. Resistance In a conductor, the voltage applied across the ends of the conductor is proportional to the current through the conductor The constant of proportionality is the resistance of the conductor

64. Fig. 17-CO, p.568

65. Resistance, cont Units of resistance are ohms (Ω) 1 Ω = 1 V / A Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor

66. Ohm’s Law Experiments show that for many materials, including most metals, the resistance remains constant over a wide range of applied voltages or currents This statement has become known as Ohm’s Law ΔV = I R Ohm’s Law is an empirical relationship that is valid only for certain materials Materials that obey Ohm’s Law are said to be ohmic

67. Resistivity The resistance of an ohmic conductor is proportional to its length, L, and inversely proportional to its cross- sectional area, A ρ is the constant of proportionality and is called the resistivity of the material

68. Table 17-1, p.576

69. Temperature Variation of Resistivity For most metals, resistivity increases with increasing temperature With a higher temperature, the metal’s constituent atoms vibrate with increasing amplitude The electrons find it more difficult to pass through the atoms

70. Temperature Variation of Resistivity, cont For most metals, resistivity increases approximately linearly with temperature over a limited temperature range ρ is the resistivity at some temperature T ρ o is the resistivity at some reference temperature T o T o is usually taken to be 20° C = 68 ° F  is the temperature coefficient of resistivity

71. Temperature Variation of Resistance Since the resistance of a conductor with uniform cross sectional area is proportional to the resistivity, you can find the effect of temperature on resistance

72. Electrical Energy and Power, cont The rate at which the energy is lost is the power From Ohm’s Law, alternate forms of power are

73. Electrical Energy and Power, final The SI unit of power is Watt (W) I must be in Amperes, R in ohms and V in Volts The unit of energy used by electric companies is the kilowatt-hour This is defined in terms of the unit of power and the amount of time it is supplied 1 kWh = 3.60 x 10 6 J

74. Fig. Q18-13, p.616

75. More About the Junction Rule I 1 = I 2 + I 3 From Conservation of Charge Diagram b shows a mechanical analog

76. RC Circuits A direct current circuit may contain capacitors and resistors, the current will vary with time When the circuit is completed, the capacitor starts to charge The capacitor continues to charge until it reaches its maximum charge (Q = Cε) Once the capacitor is fully charged, the current in the circuit is zero

77. Charging Capacitor in an RC Circuit The charge on the capacitor varies with time q = Q(1 – e -t/RC ) The time constant, =RC The time constant represents the time required for the charge to increase from zero to 63.2% of its maximum

78. Notes on Time Constant In a circuit with a large time constant, the capacitor charges very slowly The capacitor charges very quickly if there is a small time constant After t = 10 , the capacitor is over 99.99% charged

79. Household Circuits The utility company distributes electric power to individual houses with a pair of wires Electrical devices in the house are connected in parallel with those wires The potential difference between the wires is about 120V

80. Effects of Various Currents 5 mA or less Can cause a sensation of shock Generally little or no damage 10 mA Hand muscles contract May be unable to let go a of live wire 100 mA If passes through the body for just a few seconds, can be fatal