1. 1 Physics for Scientists and Engineers Chapter 22: The Electric Field II: Continuous Charge Distributions Copyright © 2004 by W. H. Freeman & Company Paul A. Tipler Gene Mosca Fifth Edition

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6. 6 Effect of Symmetry

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20. 20 22-2 Gauss’s Law

21. 21 Gauss’s Law Electric Flux Charge Distribution Relationship between field lines and charge

22. 22 Electric Flux E varies with density of lines Flux is #lines crossing a specific area Flux and “Flow” Symbol  Units: N·m 2 /C Product of Field and Area Can be + or -

23. 23 Electric Flux (cont.) Flux + when leaving a closed surface Flux - when entering a closed surface

24. 24 Electric Flux (cont.) Notice that there is no charge inside and, Net Flux is zero

25. 25 Case where E is spatially uniform:  = E·A (E factored out of integral)  = +EA (E parallel to A)  = -EA (E anti-parallel to A)

26. 26 Flux through both surfaces is identical

27. 27 Flux and Charge Amount and sign of a charge can be determined by (#lines leaving) – (#lines entering)

28. 28 (#lines leaving) – (#lines entering) = 0 net charge enclosed is zero

29. 29 net 8 lines leaving = net +q enclosed (with 8 lines per q)

30. 30 Flux due to a point Q

31. 31 Net Flux not dependent on shape of enclosing surface or any charges outside the enclosure Net Flux does depend on amount of charge inside enclosure

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33. 33 Cylindrical can enclosing part of an “infinite” plane of Q.

34. 34 Net flux = EA + EA + 0 = 2EA == 4  kq E = 4  kq/2A = 2  k(q/A) = 2  k . Plane of Charge cont.

35. 35 Gauss’s Law Permittivity of a vacuum, Gauss’s Law Gauss’s Law in terms of Permittivity

36. 36 Spherical Shell cosine = 1 (symmetry)  = EA = Q/  o E = Q/  o A A = 4  r 2.

37. 37 any closed surface inside shell has Qenc = 0  EA ~ Q = 0  E = 0 Spherical Shell cont.

38. 38 “Field”: Concept or Reality?

39. 39 Long Line

40. 40 Uniform Spherical Volume non-zero values inside same as pt Q outside

41. 41 22-4 Discontinuity of E n

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43. 43 22-5 Charge and Field at Conductor Surfaces

44. 44 E on Conductor at surface E =  /  o E normal (perpendicular) to surface E is zero inside (with static charges)

45. 45 +Point Q inside Shell shell = neutral conductor -/+ induced on shell E ~ same as for lone +pt Q.

46. 46 Charge Distribution  Field Shape

47. 47 Summary E obtained by sum of effect of all charges charges can be point (ch21) or ‘continuous’ (ch22) E can also be obtained by use of Gauss’s Law for E, where concept of E flux is used.

48. 48 22-6 Derivation of Gauss’s Law From Coulomb’s Law

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51. 51 Problems

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