# 29. Energy and Momentum in Electromagnetic Waves

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## Learning Objectives

• To comprehend the energy and momentum flow in plane electromagnetic waves.
• To estimate the magnitude of radiation pressure under various circumstances.

## 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)

### 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: Spherical Waves

A light source at one frequency with a power output of 750 Watts radiates light of wavelength 500 nanometers uniformly in all directions. What are the maximum values of E and B for this light at a distance of 3 meters from the source.

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» iTunes U (MP4 - 16MB)
» Internet Archive (MP4 - 16MB)

A source of luminosity L exerts a radiation pressure on a cross sectional area dA at a distance R from the source. What is this radiation pressure assuming total absorption of the radiation? How is this related to the Poynting flux? If the light is totally reflected to instead of absorbed, how does this pressure change?

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» iTunes U (MP4 - 18MB)
» Internet Archive (MP4 - 18MB)

### Problem 3: Radiation Pressure from the Sun

The Sun has a luminosity of 4 x 1026 Watts. The radius of the Sun is 7 x 108 meters. What is the mean Poynting vector at the surface of the Sun? What is the radiation pressure there for full absorption? What would the radiation pressure be at 1/2 the radius of the Sun?

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» iTunes U (MP4 - 8MB)
» Internet Archive (MP4 - 8MB)

### Problem 4: Solar Sailing

The total power output of the Sun is 3.9 x 1026 Watts. How large a sail is necessary to propel a 5000 kilogram spacecraft against the gravitational force of the Sun? Using the same mathematics, compute the minimum radius of a grain of sand which can survive in the solar system.

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