Vector fields

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In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane (for instance), can be visualised as: a collection of arrows with a given magnitude and direction, each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.

The following simulations are designed to plot vector fields in 2D and 3D.

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Vector Field Plotter in 2D

Instructions:

• Change the Scale or Vectors density to provide a better visualisation of the vector field.
• Zoom In or Out (or drag the plane) to change the domain.
• Change the components of the vector field $\mathbf F=F_1\,\mathbf i+F_2\,\mathbf j$.
  

   Example: F₁=x^2*sin(y) F₂=sqrt(y^2+x)*exp(x/y)

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Vector Field Plotter in 3D

Instructions:

• Change the Scale to provide a better visualisation of the vector field.
• Use right click and drag the mouse to rotate the 3D view.
• Change the components of the vector field defined as $\mathbf F=F_1\,\mathbf i+F_2\,\mathbf j+F_3\,\mathbf k$.
  

    Example: F₁=x^2*sin(y) F₂=sqrt(y^2+z)*exp(x/y) F₃=log(x-y+z)

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Worksheet exemplar

The following file contains activities and problems associated with the simulations.

• Vector fields (pdf)
• Vector fields (tex)