1. Coulomb’s Law and Electric Field Chapter 24: all Chapter 25: all

2. 2 Electric charge Able to attract other objects Two kinds Positive – glass rod rubbed with silk Negative – plastic rod rubbed with fur Like charges repel Opposite charge attract Charge is not created, it is merely transferred from one material to another Physics chapters 24 - 25

3. 3 Elementary particles Proton – positively charged Electron – negatively charged Neutron – no charge Nucleus – in center of atom, contains protons and neutrons Quarks – fundamental particles – make up protons and neutrons, have fractional charge Physics chapters 24 - 25

4. 4 ions Positive ions – have lost one or more electrons Negative ions – have gained one or more electrons Only electrons are lost or gained under normal conditions Physics chapters 24 - 25

5. 5 Conservation of charge The algebraic sum of all the electric charges in any closed system is constant. Physics chapters 24 - 25

6. 6 Electrical interactions Responsible for many things The forces that hold molecules and crystals together Surface tension Adhesives Friction Physics chapters 24 - 25

7. 7 Conductors Permit the movement of charge through them Electrons can move freely Most metals are good conductors Physics chapters 24 - 25

8. 8 Insulators Do not permit the movement of charge through them Most nonmetals are good insulators Electrons cannot move freely Physics chapters 24 - 25

9. 9 Charging by induction See pictures on pages 539-540 Physics chapters 24 - 25

10. 10 Coulomb’s Law Point charge – has essentially no volume The electrical force between two objects gets smaller as they get farther apart. The electrical force between two objects gets larger as the amount of charge increases Physics chapters 24 - 25

11. 11 Coulomb’s Law r is the distance between the charges q 1 and q 2 are the magnitudes of the charges k is a constant 8.99 x 10 9 N∙m 2 /C 2 Physics chapters 24 - 25

12. 12 Coulombs SI unit of charge, abbreviated C Defined in terms of current – we will talk about this later Physics chapters 24 - 25

13. 13 Coulomb’s law constant k is defined in terms of the speed of light k = 10 -7 c k = 1/4    0 is another constant that will be more useful later  0 = 8.85 x 10 -12 C 2 /N∙m 2 Physics chapters 24 - 25

14. 14 The coulomb Very large amount of charge Charge on 6 x 10 18 electrons Most charges we encounter are between 10 -9 and 10 -6 C 1  C = 10 -6 C Physics chapters 24 - 25

15. 15 Examples See pages 543 - 546 Physics chapters 24 - 25

16. 16 Electric Field A field is a region in space where a force can be experienced.A field is a region in space where a force can be experienced. Or: a region in space where a quantity has a definite value at every point.Or: a region in space where a quantity has a definite value at every point. Physics chapters 24 - 25

17. 17 Electric Field Produced by a charged particle.Produced by a charged particle. The force felt by another charged particle is caused by the electric field.The force felt by another charged particle is caused by the electric field. We can check for an electric field with a test charge, q t. If it experiences a force, there is an electric field.We can check for an electric field with a test charge, q t. If it experiences a force, there is an electric field. Physics chapters 24 - 25

18. 18 Electric field The definite quantity is a ratio of the electric force experienced by a charge to the amount of the charge.The definite quantity is a ratio of the electric force experienced by a charge to the amount of the charge. Vector quantity measured in N/C.Vector quantity measured in N/C. Physics chapters 24 - 25

19. 19 Electric field To determine the field from a point charge, Q, we place a test charge, q t, at some position and determine the force acting on it.To determine the field from a point charge, Q, we place a test charge, q t, at some position and determine the force acting on it. Qqtqt F Physics chapters 24 - 25

20. 20 Direction of E If the test charge is positive, E has the same direction as F.If the test charge is positive, E has the same direction as F. If the test charge is negative, E has the opposite direction as F.If the test charge is negative, E has the opposite direction as F. Physics chapters 24 - 25

21. 21 Electric Field - Point Charge Physics chapters 24 - 25

22. 22 Electric Field The field is there, independent of a test charge or anything else!The field is there, independent of a test charge or anything else! The electric field vector points in the direction a positive charge would be forced.The electric field vector points in the direction a positive charge would be forced. Physics chapters 24 - 25

23. 23 Example 1 Two charges, Q 1 = +2 x 10 -8 C and Q 2 = +3 x 10 -8 C are 50 mm apart as shown below.Two charges, Q 1 = +2 x 10 -8 C and Q 2 = +3 x 10 -8 C are 50 mm apart as shown below. What is the electric field halfway between them?What is the electric field halfway between them? Q1Q1 Q2Q2 50 mm E1E1 E2E2 Physics chapters 24 - 25

24. 24 Example 1 At the halfway point, r 1 = r 2 = 25 mm.At the halfway point, r 1 = r 2 = 25 mm. Magnitudes of fields:Magnitudes of fields: Physics chapters 24 - 25

25. 25 Example 1 E 1 = 2.9 x 10 5 N/CE 1 = 2.9 x 10 5 N/C E 2 = 4.3 x 10 5 N/CE 2 = 4.3 x 10 5 N/C E 1 is to the right and E 2 is to the left.E 1 is to the right and E 2 is to the left. E 1 = 2.9 x 10 5 N/CE 1 = 2.9 x 10 5 N/C E 2 = - 4.3 x 10 5 N/CE 2 = - 4.3 x 10 5 N/C E = E 1 + E 2 = - 1.4 x 10 5 N/CE = E 1 + E 2 = - 1.4 x 10 5 N/C Physics chapters 24 - 25

26. 26 Example 2 For the charges in Example 1, where is the electric field equal to zero?For the charges in Example 1, where is the electric field equal to zero? Since the fields are in opposite directions between the charges, the point where the field is zero must be between them.Since the fields are in opposite directions between the charges, the point where the field is zero must be between them. Q1Q1 Q2Q2 E1E1 E2E2 Physics chapters 24 - 25

27. 27 Example 2 r 1 + r 2 = s, so r 2 = s – r 1 Physics chapters 24 - 25

28. 28 Example 2 Physics chapters 24 - 25

29. 29 Field Diagrams To represent an electric field we use lines of force or field lines.To represent an electric field we use lines of force or field lines. These represent the sum of the electric field vectors.These represent the sum of the electric field vectors. Physics chapters 24 - 25

30. 30 Field Diagrams Physics chapters 24 - 25

31. 31 Field Diagrams Physics chapters 24 - 25

32. 32 Field Diagrams At any point on the field lines, the electric field vector is along a line tangent to the field line.At any point on the field lines, the electric field vector is along a line tangent to the field line. Physics chapters 24 - 25

33. 33 Field Diagrams Physics chapters 24 - 25

34. 34 Field Diagrams Lines leave positive charges and enter negative charges. Lines leave positive charges and enter negative charges. Lines are drawn in the direction of the force on a positive test charge.Lines are drawn in the direction of the force on a positive test charge. Lines never cross each other.Lines never cross each other. The spacing of the lines represents the strength or magnitude of the electric field.The spacing of the lines represents the strength or magnitude of the electric field. Physics chapters 24 - 25

35. 35 Point Charges Lines leave or enter the charges in a symmetric pattern.Lines leave or enter the charges in a symmetric pattern. The number of lines around the charge is proportional to the magnitude of the charge.The number of lines around the charge is proportional to the magnitude of the charge. Physics chapters 24 - 25

36. 36 Point Charges Physics chapters 24 - 25

37. 37 Point Charges Physics chapters 24 - 25

38. 38 Gauss’s Law Electric flux through a closed surface is proportional to the total number of field lines crossing the surface in the outward direction minus the number crossing in the inward direction.Electric flux through a closed surface is proportional to the total number of field lines crossing the surface in the outward direction minus the number crossing in the inward direction. Physics chapters 24 - 25

39. 39 Example 25-9 (see page 563) Field of a charged sphere is the same as if it were a point charge Physics chapters 24 - 25

40. 40 Example 25-10 (see page 564) Field of a infinite line of charge is Physics chapters 24 - 25

41. 41 Other scenarios See table on page 567See table on page 567 Physics chapters 24 - 25

42. 42 Example 3 Two parallel metal plates are 2 cm apart.Two parallel metal plates are 2 cm apart. An electric field of 500 N/C is placed between them.An electric field of 500 N/C is placed between them. An electron is projected at 10 7 m/s halfway between the plates and parallel to them.An electron is projected at 10 7 m/s halfway between the plates and parallel to them. How far will the electron travel before it strikes the positive plate?How far will the electron travel before it strikes the positive plate? Physics chapters 24 - 25

43. 43 Example 3 Two charged parallel plates create a uniform electric field in the space between them.Two charged parallel plates create a uniform electric field in the space between them. Physics chapters 24 - 25

44. 44 Example 3 E vovo This is just like a projectile problem except that the acceleration is not a given value. Physics chapters 24 - 25

45. 45 Example 3 = 8.8 x 10 13 m/s 2 Physics chapters 24 - 25

46. 46 Example 3 8.8 x 10 13 m/s 2 is the vertical acceleration of the electron.8.8 x 10 13 m/s 2 is the vertical acceleration of the electron. Horizontally, the acceleration is zero.Horizontally, the acceleration is zero. x = vtx = vt v = 1 x 10 7 m/s & t = ?v = 1 x 10 7 m/s & t = ? Physics chapters 24 - 25

47. 47 Example 3 Back to vertical direction:Back to vertical direction: y = y o + v o t + 1 / 2 at 2y = y o + v o t + 1 / 2 at 2 y = 1 / 2 at 2y = 1 / 2 at 2 = 1.5 x 10 -8 s Physics chapters 24 - 25

48. 48 Example 3 Back to horizontal direction:Back to horizontal direction: x = vtx = vt x = (1 x 10 7 m/s)(1.5 x 10 –8 s)x = (1 x 10 7 m/s)(1.5 x 10 –8 s) x = 0.15 m = 15 cmx = 0.15 m = 15 cm Physics chapters 24 - 25

49. 49 Dipoles A pair of charges with equal and opposite sign.A pair of charges with equal and opposite sign. Induced dipoles, molecular dipoles, etc.…Induced dipoles, molecular dipoles, etc.… Physics chapters 24 - 25