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## Visualizing Electromagnetic Plane Waves: Instructor's Guide

### Main Ideas

• Representations of plane waves

Estimated Time:

### Activity: Introduction

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, $\vec{k}$.

### Activity: Wrap-up

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.

### Extensions

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.

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