# 28. Maxwell's Equations and Electromagnetic Waves

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## Learning Objectives

• To look at the full set of Maxwell's Equations.
• To understand the properties of electromagnetic waves as predicted by Maxwell's Equations in a vacuum.
• To consider the wave equation and to comprehend the nature of solutions to this equation.
• To comprehend the meaning of standing waves as contrasted to traveling waves.

## Preparation

### Course Notes

Read through the course notes before watching the video.  The course note files may also contain links to associated animations or interactive simulations.

Maxwell's Equations and Electromagnetic Waves (PDF - 1.1MB)

## Lecture Video

### Video Excerpts

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## Learning Activities

### Guided Activities

Read through the class slides. They explain all of the concepts from the module.

Slides (PDF)

### Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems.

### Concept Questions

Concept Questions (PDF)

Solutions (PDF)

### Challenge Problems

Challenge Problems (PDF)

Solutions (PDF)

## Problem Solving Help

Watch the Problem Solving Help videos for insights on how to approach and solve problems related to the concepts in this module.

### Problem 1: An Electromagnetic Plane Wave

An electromagnetic wave has a frequency of 4 x 1013 Hz. The wave travels in the +y direction and the magnetic field B is along the x-axis with an amplitude of 7.3 x 10-4 Tesla. What are the vector equations for E and B?

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» iTunes U (MP4 - 23MB)
» Internet Archive (MP4 - 23MB)

### Problem 2: Standing Waves

A standing electromagnetic wave has a frequency of 600 x 106 Hz. It is positioned between two conducting planes a distance of 75 centimeters apart. At what positions between the planes could a point charge be placed at rest so that it would remain at rest? What is the Poynting vector for a standing wave?

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