Fundamentals of Electricity and Magnetism

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, |q1|and |q2|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, • ke is called the Coulomb Constant • ke = 8.9875 x 109 N m2/C2 • 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

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 q1 on q3 is • The force exerted by q2 on q3 is • The total force exerted on q3 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 GraaffGenerator • 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 • V1 is the electric potential due to q1 at some point P • The work required to bring q2 from infinity to P without acceleration is q2V1 • 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 DVcap = DVbattery • Demo 2

48. Capacitors in Parallel • The total charge is equal to the sum of the charges on the capacitors • Qtotal = Q1 + Q2 • 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