# 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.

## Preparation

### Course Notes

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

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.

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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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