3. Electric Fields and Discrete Charge Distributions

• 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
• Download Course Materials

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Learning Objectives

• To be able calculate the electric field at every point in space given a set of point electric charges and their locations.
• To comprehend the various ways in which we charge objects and explain them in words.
• To comprehend the nature of the electric field of an electric dipole and to recognize what is meant when we go to the limit of a perfect point dipole.
• To be able to describe why we put so much emphasis on the properties of electric dipoles.
• To be able to describe when an electric dipole immersed in an external electric field will experience a torque and a force.

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 2.1 through 2.8:
Coulomb'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 video for insights on how to approach and solve problems related to the concepts in this module.

Problem: An Electric Dipole

We have a charge +q located at aî on the positive x-axis, and a charge –q located at -aî on the negative x-axis. Find the electric field everywhere in space. Using your general expression, find the electric field at a distance r»a far from the origin. Show that at this distance the electric falls off as inverse r cubed.

Related Visualizations

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

• Interactive Molecules 2D
• The Electric Field of a Dipole
• Torque on an Electric Dipole in a Constant Field
• Van de Graaff Visualizations
• E Field Configurations
• The Line of Charge
  
• The Charged Ring

 

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