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# Gauss's Law

**Keywords:**Small Group Activity, Compare and Contrast, Electric Field, Gauss' Law, Vector Field, Symmetry, Proof by Contradiction

### Highlights of the activity

- This small group activity is designed to help students practice using the symmetry arguments necessary to use Gauss's Law.
- Students are asked to find the electric field using Gauss's Law for either a spherically or cylindrically symmetric charge density and must make explicit symmetry arguments using Proof by Contradiction as part of their solution.
- The compare and contrast discussion on the symmetry focuses on the fact that all examples have zero field inside the shell, different answers within the shell, and answers that depend only on the total charge on the shell for points outside the shell.

### Reasons to spend class time on the activity

This activity gets students using symmetry arguments in a more sophisticated way and has students develop deeper understanding of the implications of Gauss's Law.