• Representations of plane waves

Estimated Time:

• Computers with Mathematica/Maple

Students visualize electromagnetic plane waves using either a Mathematica (or Maple) worksheet by exploring the electric and magnetic field vectors of a given electromagnetic plane wave by choosing the wave vector $\vec{k}$ themselves. This computer visualization shows all of the aspects of electromagnetic plane waves–the electric and magnetic field vectors at planes in space specified by a chosen wave vector, $\vec{k}$.

The whole class wrap-up discussion summarizes how the electric field, magnetic field, and wave vectors are related, allowing students to visualize what is planar about electromagnetic plane waves.

This activity is part of the Plane Wave Sequence. The following activities are included within this sequence:

• Preceding activities:
  • Recall the Dot Product: This small whiteboard question prompts students to recall something they recall regarding the dot product.
  • Visualizing Plane Waves: In this small group activity, students calculate $\vec{k}\cdot\vec{r}$ for a given $\vec{k}$ for each point on a grid and then connect points with constant value of $\vec{k}\cdot\vec{r}$.
  • Scalar Plane Waves: This computer visualization activity uses color to represent various plane waves chosen by a particular wave vector $\vec{k}$ in three-dimensions.

• Follow-up activity:
  • Comparing Representations of Plane Waves: This activity can be used as a homework problem or as a small group activity where students analyze multiple representations of plane waves, noting which features are present and which are ignored in each representation.