4. Electrostatic force due to spherical shell of charge r R z

5. x y  

6. Spherical coordinates

7. x y     0 to  z

8. x y    0 to 2  r  0 to R z

9. x y   z

10. Electrostatic force due to spherical shell of charge r R z q0q0

11. R z r

12. R z r

13. R z r

14. R z r

15. R z r

16. R z r

17. R z r

18. R z r

19. R z r

20. R z r

21. R z r

22. R z r  

23. R z r  

24. R z r   Only z-component survives

25. Electrostatic force due to spherical shell of charge R z r   Rcos  Why are we doing this? To change variable to  which is the polar angle

26. Electrostatic force due to spherical shell of charge R z r   Rcos 

27. r and  are NOT independent

28. Electrostatic force due to spherical shell of charge R z   r

29. R z r   r

30. R z   r

31. R z r  

32. Law of cosines

33. Electrostatic force due to spherical shell of charge R z r  

36. R z r

37. R z r

38. R z r

39. R z r

40. R z r

41. R z r

42. R z r

43. R z r

44. R z r

45. R z r

46. R z r

47. R z r

48. R z r

49. R z r

50. R z r

51. R z r

52. R z r

53. R z r

54. R z r r = z - R

55. Electrostatic force due to spherical shell of charge R z r r = z + R

56. Electrostatic force due to spherical shell of charge

58. Electrostatic force due to spherical shell of charge (inside the shell) R z r r = R - z

59. Electrostatic force due to spherical shell of charge (inside the shell) R z r r = R + z

60. Electrostatic force due to spherical shell of charge (inside the shell)