4. Electric Fields and Continuous 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 understand the nature of the common continuous charge distributions with which we deal: lines of charge, planes of charge, and spheres of charge.
• To be able calculate the electric field at every point in space given a continuous distribution of charge.

Preparation

Course Notes

Read through the course notes. The course note files may also contain links to associated animations or interactive simulations.

Read sections 2.9 through 2.14:
Coulomb's Law (PDF)

Learning Activities

Guided Activities

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

Slides (PDF)

Self-Assessment

Once you have reviewed all the materials, try the Challenge Problems.

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: Calculating the Potential of a Semi-circular Rod by Integration

We distribute a total charge Q uniformly on a thin insulating rod bent into a semi-circular of radius a. Calculate the electric field at the center of radius of the semi-circle. Calculate the electric field at the same point.

Problem 2: 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.

Related Visualizations

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

• Integrating Along a Line of Charge
• The Line of Charge
• Integrating Around a Ring of Charge
• The Charged Ring

 

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