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Understanding Electrostatic Force in Spherical Coordinates

Explore the theory and calculations of electrostatic force due to spherical shells of charge in spherical coordinates. Learn how to calculate forces along different axes. Discover laws of cosines and the importance of variable changes in physics.

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Understanding Electrostatic Force in Spherical Coordinates

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

  2. y  x

  3. Spherical coordinates

  4. z   0 to   y  x

  5. z •  0 to    0 to 2 r  0 to R y  x

  6. y  x z

  7. Electrostatic force due to spherical shell of charge r R q0 z

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

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

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

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

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

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

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

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

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

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

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

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

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

  21. Electrostatic force due to spherical shell of charge r R   z Only z-component survives

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

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

  24. r and  are NOT independent

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

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

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

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

  29. Law of cosines

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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