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Line Integrals of Vector Fields: Flux

Line Integrals of Vector Fields: Flux
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2016-11-07 13:38
VectorFunctionCoordinate GeometryCalculusIntegral
This example demonstrates line integrals of vector fields, focusing on the concept of flux. Key mathematical concepts include vector fields, line integrals, and flux. Using GeoGebra commands, it illustrates how to construct vector fields, path integrals, and flux calculations. Suitable for advanced students or teachers in calculus courses.

GeoGebra Commands & Parameters

  1. SelectedIndex(pathNames) → pathIndex
  2. Midpoint(N, P) → Q
  3. Element(pathList, pathIndex) → path
  4. Derivative(path) → DDpath
  5. ParametricDerivative(path) → Dpath
  6. Distance(N, P) → NP
  7. Element(CompX, pathIndex) → RTX
  8. Derivative(RTX, x) → DRTX
  9. Element(CompY, pathIndex) → RTY
  10. Derivative(RTY, x) → DRTY
  11. CurveCartesian(x(path(t)), y(path(t)), t, 0, s) → partPath
  12. Integral(MUL, 0, 1) → Flux
  13. Textfield(F_1) → InputBox1
  14. Textfield(F_2) → InputBox2
  15. Segment(path(0.3), path(0.3 + 0.01)) → arrow1
  16. Segment(path(0.6), path(0.6 + 0.01)) → arrow2
  17. If(Flux ≟ Flux, Flux, Sum[Sequence[(((F_1(x(path(i + dS / 2)), y(path(i + dS / 2))), F_2(x(path(i + dS / 2)), y(path(i + dS / 2)))) * (y(Dpath(i + dS / 2)), (-x(Dpath(i + dS / 2))))) * dS), i, 0, s - dS, dS]]) → FLUUX
  18. Sequence(Vector[path(i), path(i) + ((scale * F_1(x(path(i)), y(path(i)))), (scale * F_2(x(path(i)), y(path(i)))))], i, 0, s, 0.15) → PathVectors
  19. Sequence(path(i), i, 0.25, 0.75, 0.25) → PtPathList
  20. Sequence(Vector[(0, 0), (1 / sqrt((y(DDpath(i)))^(2) + (x(DDpath(i)))^(2)) * (y(DDpath(i)), (-x(DDpath(i)))))], i, 0.25, 0.75, 0.25) → norvectorsList
  21. Translate(Vector[Element[norvectorsList, 1]], Element[PtPathList, 1]) → u
  22. Translate(Vector[Element[norvectorsList, 2]], Element[PtPathList, 2]) → v
  23. Translate(Vector[Element[norvectorsList, 3]], Element[PtPathList, 3]) → w
  24. Textfield(xA) → InputBox3
  25. Textfield(yA) → InputBox4
  26. Textfield(xB) → InputBox5
  27. Textfield(yB) → InputBox6