29. Energy and Momentum in Electromagnetic Waves

• Course Home
• Syllabus
• Electric Fields

  • 1. Introduction to Electric Fields
  • 2. Math Review, Fields
  • 3. Electric Fields and Discrete Charge Distributions
  • 4. Electric Fields and Continuous Charge Distributions
  • 5. Gauss's Law
• Electric Potential

  • 6. Discrete and Continuous Distributions of Charge
  • 7. Equipotential Lines and Electric Fields
  • 8. Gauss's Law and Configuration Energy
• Capacitors

  • 9. Conductors and Insulators, Conductors as Shields
  • 10. Capacitance and Capacitors, Energy Stored in Capacitors
  • 11. Capacitors and Dielectrics
• Circuits

  • 12. Current, Current Density, Resistance, and Ohm's Law
  • 13. Batteries and Circuit Elements
  • 14. DC Circuits
  • 15. DC Circuits with Capacitors
• Magnetic Fields and Forces

  • 16. Magnetic Field
  • 17. Magnetic Forces
  • 18. Magnetic Dipoles
• Creating Magnetic Fields

  • 19. Biot-Savart Law
  • 20. Ampere's Law
• Faraday's Law

  • 21. Faraday's Law
  • 22. Inductance and Magnetic Energy
  • 23. RL Circuits
• Oscillating Circuits

  • 24. Undriven RLC Circuits
  • 25. Driven RLC Circuits
• Maxwell's Equations

  • 26. The Displacement Current and Maxwell's Equations
  • 27. Poynting Vector and Energy Flow in a Capacitor
• Electromagnetic Waves

  • 28. Maxwell's Equations and Electromagnetic Waves
  • 29. Energy and Momentum in Electromagnetic Waves
  • 30. Generating EM Waves, Dipole Radiation and Polarization
• Nature of Light

  • 31. Interference
  • 32. Diffraction
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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.

Read sections 13.7 through 13.14:
Maxwell's Equations and Electromagnetic Waves (PDF - 1.1MB)

Lecture Video

Video Excerpts

Learning Activities

Guided Activities

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

Slides (PDF)

Self-Assessment

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.

Problem 2: Radiation Pressure

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?

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?

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.

Related Visualizations

The visualizations linked below are related to the concepts covered in this module.

• Dipole Radiation
• Dipole Radiation Reversing
• Radiation Pattern of a Quarter Wave Antenna
• Radiation from a Quarter Wave Antenna
• Generating Plane Wave Radiation

 

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