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Coulomb’s Law and Electric Field

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

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Coulomb’s Law and Electric Field

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

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

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

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

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

  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. Coulomb’s Law • r is the distance between the charges • q1 and q2 are the magnitudes of the charges • k is a constant • 8.99 x 109 N∙m2/C2 Physics chapters 24 - 25

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

  13. Coulomb’s law constant • k is defined in terms of the speed of light • k = 10-7c • k = 1/4pe0 • e0 is another constant that will be more useful later • e0 = 8.85 x 10-12 C2/N∙m2 Physics chapters 24 - 25

  14. The coulomb • Very large amount of charge • Charge on 6 x 1018 electrons • Most charges we encounter are between 10-9 and 10-6 C • 1 mC = 10-6 C Physics chapters 24 - 25

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

  16. Electric Field • 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. Physics chapters 24 - 25

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

  18. Electric field • 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. Physics chapters 24 - 25

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

  20. Direction of E • 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. Physics chapters 24 - 25

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

  22. Electric Field • 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. Physics chapters 24 - 25

  23. Example 1 • Two charges, Q1 = +2 x 10-8 C and Q2 = +3 x 10-8 C are 50 mm apart as shown below. • What is the electric field halfway between them? E1 E2 Q2 Q1 50 mm Physics chapters 24 - 25

  24. Example 1 • At the halfway point, r1 = r2 = 25 mm. • Magnitudes of fields: Physics chapters 24 - 25

  25. Example 1 • E1 = 2.9 x 105 N/C • E2 = 4.3 x 105 N/C • E1 is to the right and E2 is to the left. • E1 = 2.9 x 105 N/C • E2 = - 4.3 x 105 N/C • E = E1 + E2 = - 1.4 x 105 N/C Physics chapters 24 - 25

  26. Example 2 • 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. E1 E2 Q2 Q1 Physics chapters 24 - 25

  27. Example 2 r1 + r2 = s, so r2 = s – r1 Physics chapters 24 - 25

  28. Example 2 Physics chapters 24 - 25

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

  30. Field Diagrams Physics chapters 24 - 25

  31. Field Diagrams Physics chapters 24 - 25

  32. Field Diagrams • 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. Field Diagrams Physics chapters 24 - 25

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

  35. Point Charges • 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. Physics chapters 24 - 25

  36. Point Charges Physics chapters 24 - 25

  37. Point Charges Physics chapters 24 - 25

  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. Physics chapters 24 - 25

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

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

  42. Example 3 • Two parallel metal plates are 2 cm apart. • An electric field of 500 N/C is placed between them. • An electron is projected at 107 m/s halfway between the plates and parallel to them. • How far will the electron travel before it strikes the positive plate? Physics chapters 24 - 25

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

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

  45. Example 3 = 8.8 x 1013 m/s2 Physics chapters 24 - 25

  46. Example 3 • 8.8 x 1013 m/s2 is the vertical acceleration of the electron. • Horizontally, the acceleration is zero. • x = vt • v = 1 x 107 m/s & t = ? Physics chapters 24 - 25

  47. Example 3 • Back to vertical direction: • y = yo + vot + 1/2at2 • y = 1/2at2 = 1.5 x 10-8 s Physics chapters 24 - 25

  48. Example 3 • Back to horizontal direction: • x = vt • x = (1 x 107 m/s)(1.5 x 10–8 s) • x = 0.15 m = 15 cm Physics chapters 24 - 25

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

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