5. Gauss's Law

• 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 be able to recognize an open surface and describe how it is different from a closed surface.
• To understand what is meant by the flux of a vector field through an open or a closed surface.
• To comprehend the meaning of Gauss's Law.
• To use Gauss's Law to calculate electric fields in situations with high degrees of symmetry: planar, cylindrical, and spherical.

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.

Gauss's Law (PDF)

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: The Electric Field of a Line of Charge

A long straight wire carries a charge per unit length λ. What is the electric field a distance d from the wire? Find this field in two different ways, first using Coulomb's Law, and then using Gauss's Law.

Problem 2: Conducting Spherical Shell Carrying Charge, with a Point Charge at the Center

A conducting spherical shell has an inner radius and an outer radius b. We place a positive point charge +Q at its center. We also place a total charge of -3Q on the thick shell. Find the electric field everywhere. What is the charge on the inner surface of the shell? What is the charge on the outer surface? Determine the electric potential everywhere in space, assuming that the potential is zero at infinity.

Related Visualizations

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

• Charge Moving in a Constant Field
• The Force on a Charge in a Time-Changing Field
• Repulsion of Charges with Opposite Sign

 

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