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Activities

Small Group Activity

5 min.

Acting Out Flux
Students hold rulers and meter sticks to represent a vector field. The instructor holds a hula hoop to represent a small area element. Students are asked to describe the flux of the vector field through the area element.
  • flux electrostatics vector fields
    Found in: AIMS Maxwell, Static Fields, Surfaces/Bridge Workshop, Problem-Solving course(s) Found in: Gauss/Ampere Sequence (Integral Form), Flux Sequence sequence(s)

Computer Simulation

30 min.

Visualizing Flux through a Cube
Students explore the effects of putting a point charge at various places inside, outside, and on the surface of a cubical Gaussian surface. The Mathematica worksheet or Sage activity shows the electric field due to the charge, then plots the the flux integrand on the top surface of the box, calculates the flux through the top of the box, and the value of the flux through the whole cube.
  • Found in: Static Fields, AIMS Maxwell, Surfaces/Bridge Workshop, Problem-Solving course(s) Found in: Gauss/Ampere Sequence (Integral Form), Geometry of Vector Fields Sequence, Flux Sequence sequence(s)

Small Group Activity

30 min.

Flux through a Cone
Students calculate the flux from the vector field \(\vec{F} = C\, z\, \hat{z}\) through a right cone of height \(H\) and radius \(R\) .
  • Found in: Static Fields, AIMS Maxwell course(s) Found in: Integration Sequence, Flux Sequence sequence(s)

Find the upward pointing flux of the electric field \(\vec E =E_0\, z\, \hat z\) through the part of the surface \(z=-3 s^2 +12\) (cylindrical coordinates) that sits above the \((x, y)\)--plane.

  • Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s) Found in: Flux Sequence, Paraboloid Sequence sequence(s)
Find the upward pointing flux of the vector field \(\boldsymbol{\vec{H}}=2z\,\boldsymbol{\hat{x}} +\frac{1}{x^2+1}\boldsymbol{\hat{y}}+(3+2z)\boldsymbol{\hat{z}}\) through the rectangle \(R\) with one edge along the \(y\) axis and the other in the \(xz\)-plane along the line \(z=x\), with \(0\le y\le2\) and \(0\le x\le3\).
  • Found in: AIMS Maxwell, Static Fields, Problem-Solving course(s)

Small Group Activity

30 min.

Visualization of Divergence
Students predict from graphs of simple 2-d vector fields whether the divergence is positive, negative, or zero in various regions of the domain using the geometric definition of the divergence of a vector field at a point as flux per unit volume (here: area) through an infinitesimal box surrounding that point. Optionally, students can use computer algebra to verify their predictions.
  • Found in: Static Fields, AIMS Maxwell, Vector Calculus II, Surfaces/Bridge Workshop, Problem-Solving course(s) Found in: Geometry of Vector Fields Sequence, Flux Sequence sequence(s)

Small Group Activity

30 min.

The Fishing Net
Students compute surface integrals and explore their interpretation as flux.
  • Found in: Vector Calculus II, Surfaces/Bridge Workshop course(s) Found in: Workshop Presentations 2023 sequence(s)