28. Maxwell's Equations and Electromagnetic Waves

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• 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 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.

Read sections 13.2 through 13.6:
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

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?

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?

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
  
• The Electric and Magnetic Fields of a Plane Wave

 

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