# 5. Gauss's Law

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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

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## 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.

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» iTunes U (MP4 - 26MB)
» Internet Archive (MP4 - 26MB)

### 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.

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