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平衡表面电荷分布

平衡表面电荷分布
几何画板及绘图内容加载中，请稍等……
2018-11-01 10:08
立体几何微积分积分
这个范例演示了平衡表面电荷分布的图形。它涉及微积分中的核心概念，如积分和导数。通过使用GeoGebra命令如CurveCartesian、Point、Union、Vector等，可以构造出复杂的三维形状。适合大学物理和数学课程使用。

GeoGebra 命令及参数

  1. CurveCartesian((a * cos(q)), (b * sin(q)), q, skip, π / 2 - skip) → d
  2. Point(d) → A
  3. CurveCartesian((a * cos(q)), (b * sin(q)), q, acos(x(A) / a) + skip, π / 2 - skip) → e
  4. Point(e) → B
  5. CurveCartesian((a * cos(q)), (b * sin(q)), q, acos(x(B) / a) + skip, π / 2 - skip) → f
  6. Point(f) → C
  7. CurveCartesian((a * cos(q)), (b * sin(q)), q, acos(x(C) / a) + skip, π / 2 - skip) → g
  8. Point(g) → D
  9. CurveCartesian((a * cos(q)), (b * sin(q)), q, acos(x(D) / a) + skip, π / 2 - skip) → h
  10. Point(h) → E
  11. Union(Union[Mirror[orig, yAxis], Mirror[orig, (0, 0)]], Mirror[orig, xAxis]) → reflections
  12. Vector(A, A + Sum[Sequence[(kqsq * Vector[Element[reflections, k], A] / Distance[A, Element[reflections, k]]^(3)), k, 1, 15]] + (kqsq * Vector[B, A] / Distance[A, B]^(3)) + (kqsq * Vector[C, A] / Distance[A, C]^(3)) + (kqsq * Vector[D, A] / Distance[A, D]^(3)) + (kqsq * Vector[E, A] / Distance[A, E]^(3))) → F_A
  13. Vector(B, B + Sum[Sequence[(kqsq * Vector[Element[reflections, k], B] / Distance[B, Element[reflections, k]]^(3)), k, 1, 15]] + (kqsq * Vector[A, B] / Distance[B, A]^(3)) + (kqsq * Vector[C, B] / Distance[B, C]^(3)) + (kqsq * Vector[D, B] / Distance[B, D]^(3)) + (kqsq * Vector[E, B] / Distance[B, E]^(3))) → F_B
  14. Vector(C, C + Sum[Sequence[(kqsq * Vector[Element[reflections, k], C] / Distance[C, Element[reflections, k]]^(3)), k, 1, 15]] + (kqsq * Vector[B, C] / Distance[C, B]^(3)) + (kqsq * Vector[A, C] / Distance[C, A]^(3)) + (kqsq * Vector[D, C] / Distance[C, D]^(3)) + (kqsq * Vector[E, C] / Distance[C, E]^(3))) → F_C
  15. Vector(D, D + Sum[Sequence[(kqsq * Vector[Element[reflections, k], D] / Distance[D, Element[reflections, k]]^(3)), k, 1, 15]] + (kqsq * Vector[B, D] / Distance[D, B]^(3)) + (kqsq * Vector[C, D] / Distance[D, C]^(3)) + (kqsq * Vector[A, D] / Distance[D, A]^(3)) + (kqsq * Vector[E, D] / Distance[D, E]^(3))) → F_D
  16. Vector(E, E + Sum[Sequence[(kqsq * Vector[Element[reflections, k], E] / Distance[E, Element[reflections, k]]^(3)), k, 1, 15]] + (kqsq * Vector[B, E] / Distance[E, B]^(3)) + (kqsq * Vector[C, E] / Distance[E, C]^(3)) + (kqsq * Vector[D, E] / Distance[E, D]^(3)) + (kqsq * Vector[A, E] / Distance[E, A]^(3))) → F_E
  17. Tangent(E, c) → i,
  18. Tangent(D, c) → j,
  19. Tangent(C, c) → k,
  20. Tangent(B, c) → l,
  21. Tangent(A, c) → m,
  22. OrthogonalLine(E, i) → n
  23. OrthogonalLine(D, j) → p
  24. OrthogonalLine(C, k) → q
  25. OrthogonalLine(B, l) → r
  26. OrthogonalLine(A, m) → s
  27. Point(n) → F
  28. Point(p) → G
  29. Point(q) → H
  30. Point(r) → I
  31. Point(s) → J
  32. Ray(A, J) → t
  33. Ray(B, I) → f_1
  34. Ray(C, H) → g_1
  35. Ray(D, G) → h_1
  36. Ray(E, F) → i_1
  37. Integral(sqrt(((a * sin(x)))^(2) + ((b * cos(x)))^(2)), acosd(x(A) / a), acosd(x(B) / a)) → l2
  38. Integral(sqrt(((a * sin(x)))^(2) + ((b * cos(x)))^(2)), acosd(x(B) / a), acosd(x(C) / a)) → l3
  39. Integral(sqrt(((a * sin(x)))^(2) + ((b * cos(x)))^(2)), acosd(x(C) / a), acosd(x(D) / a)) → l4
  40. Integral(sqrt(((a * sin(x)))^(2) + ((b * cos(x)))^(2)), acosd(x(D) / a), acosd(x(E) / a)) → l5
  41. CurveCartesian((a * cos(q)), (b * sin(q)), q, (-acos(x(A) / a)), acos(x(A) / a)) → o
  42. CurveCartesian((a * cos(q)), (b * sin(q)), q, acosd(x(A) / a), acosd(x(B) / a)) → u
  43. CurveCartesian((a * cos(q)), (b * sin(q)), q, acosd(x(B) / a), acosd(x(C) / a)) → v
  44. CurveCartesian((a * cos(q)), (b * sin(q)), q, acosd(x(C) / a), acosd(x(D) / a)) → w
  45. CurveCartesian((a * cos(q)), (b * sin(q)), q, acosd(x(D) / a), acosd(x(E) / a)) → a_1
  46. CurveCartesian((a * cos(q)), (b * sin(q)), q, acosd(x(E) / a), π - acosd(x(E) / a)) → b_1