Chapter 21 Electric Charge and Electric Fields

1. Chapter 21 Electric Charge and Electric Fields • What is a field? • Why have them? • What causes fields?

2. Electric Charge • Types: • Positive • Glass rubbed with silk • Missing electrons • Negative • Rubber/Plastic rubbed with fur • Extra electrons • Arbitrary choice • convention attributed to ? • Units: amount of charge is measured in [Coulombs] • Empirical Observations: • Like charges repel • Unlike charges attract

4. Charge in the Atom • Protons (+) • Electrons (-) • Ions • Polar Molecules

5. Charge Properties • Conservation • Charge is not created or destroyed, only transferred. • The net amount of electric charge produced in any process is zero. • Quantization • The smallest unit of charge is that on an electron or proton. (e = 1.6 x 10-19 C) • It is impossible to have less charge than this • It is possible to have integer multiples of this charge

6. Conductors and Insulators • Conductor transfers charge on contact • Insulator does not transfer charge on contact • Semiconductor might transfer charge on contact

7. Charge Transfer Processes • Conduction • Polarization • Induction

8. The Electroscope

9. Coulomb’s Law • Empirical Observations • Formal Statement Direction of the force is along the line joining the two charges

10. Active Figure 23.7 (SLIDESHOW MODE ONLY)

11. Coulomb’s Law Example • What is the magnitude of the electric force of attraction between an iron nucleus (q=+26e) and its innermost electron if the distance between them is 1.5 x 10-12 m

12. Hydrogen Atom Example • The electrical force between the electron and proton is found from Coulomb’s law • Fe = keq1q2 / r2 = 8.2 x 108 N • This can be compared to the gravitational force between the electron and the proton • Fg = Gmemp / r2 = 3.6 x 10-47 N

13. Subscript Convention +q1 +q2

14. More Coulomb’s Law +q1 +q2 Coulomb’s constant: permittivity of free space: Charge polarity: Same sign Force is right Opposite sign Force is Left Electrostatics --- Charges must be at rest!

15. Superposition of Forces +Q1 +Q2 +Q0 +Q3

16. Coulomb’s Law Example • Q = 6.0 mC • L = 0.10 m • What is the magnitude and direction of the net force on one of the charges?

17. Zero Resultant Force, Example q1 = 15.0 mC • Where is the resultant force equal to zero? • The magnitudes of the individual forces will be equal • Directions will be opposite • Will result in a quadratic • Choose the root that gives the forces in opposite directions q2 = 6.0 mC

18. Electrical Force with Other Forces, Example • The spheres are in equilibrium • Since they are separated, they exert a repulsive force on each other • Charges are like charges • Proceed as usual with equilibrium problems, noting one force is an electrical force

19. Electrical Force with Other Forces, Example cont. • The free body diagram includes the components of the tension, the electrical force, and the weight • Solve for |q| • You cannot determine the sign of q, only that they both have same sign

20. The Electric Field • Charge particles create forces on each other without ever coming into contact. • “action at a distance” • A charge creates in space the ability to exert a force on a second very small charge. This ability exists even if the second charge is not present. • We call this ability to exert a force at a distance a “field” • In general, a field is defined: • The Electric Field is then: Why in the limit?

21. -Q +Q Electric Field near a Point Charge Electric Field Vectors Electric Field Lines

22. Active Figure 23.13 (SLIDESHOW MODE ONLY)

23. Rules for Drawing Field Lines • The electric field, , is tangent to the field lines. • The number of lines leaving/entering a charge is proportional to the charge. • The number of lines passing through a unit area normal to the lines is proportional to the strength of the field in that region. • Field lines must begin on positive charges (or from infinity) and end on negative charges (or at infinity). The test charge is positive by convention. • No two field lines can cross.

24. Electric Field Lines, General • The density of lines through surface A is greater than through surface B • The magnitude of the electric field is greater on surface A than B • The lines at different locations point in different directions • This indicates the field is non-uniform

25. Example Field Lines Line Charge Dipole For a continuous linear charge distribution, Linear Charge Density:

26. Active Figure 23.24 (SLIDESHOW MODE ONLY)

27. More Field Lines Surface Charge Density: Volume Charge Density:

28. Superposition of Fields +q1 +q2 P +q3

29. Superposition Example • Find the electric field due to q1, E1 • Find the electric field due to q2, E2 • E = E1 + E2 • Remember, the fields add as vectors • The direction of the individual fields is the direction of the force on a positive test charge

30. Electric Field of a Dipole y -q +q

31. Example Three point charges are arranged as shown in Figure P23.19. • Find the vector electric field that the 6.00-nC and –3.00-nC charges together create at the origin. • (b) Find the vector force on the 5.00-nC charge. Figure P23.19

32. Example Three point charges are aligned along the x axis as shown in Figure P23.52. Find the electric field at • the position (2.00, 0) and • the position (0, 2.00). Figure P23.52

33. in +x direction.

34. P23.19 (a) (b)

35. -Q +Q -e Motion of Charged Particles in a Uniform Electric Field

36. -Q +Q e Example • A proton accelerates from rest in a uniform electric field of 500 N/C. At some time later, its speed is 2.50 x 106 m/s. • Find the acceleration of the proton. • How long does it take for the proton to reach this speed? • How far has it moved in this time? • What is the kinetic energy?

37. Motion of Charged Particles in a Uniform Electric Field +Q -e -Q

38. Active Figure 23.26 (SLIDESHOW MODE ONLY)

39. +Q -Q +Q -e -e -Q Motion of Charged Particles in a Uniform Electric Field Phosphor Screen This device is known as a cathode ray tube (CRT)

40. Dipoles The combination of two equal charges of opposite sign, +q and –q, separated by a distance l -q +q

41. Dipoles in a Uniform Electric Field +q -q

42. Work Rotating a Dipole in an Uniform Electric Field +q -q