4. Electric Fields and Continuous Charge Distributions

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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.


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)


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.

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» iTunes U (MP4 - 10MB)
» Internet Archive (MP4 - 10MB)


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.

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Download this video:
» iTunes U (MP4 - 26MB)
» Internet Archive (MP4 - 26MB)

Related Visualizations

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


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