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# Ampère's Law

**Keywords:**Small Group Activity, Compare and Contrast, Magnetic Fields, Ampere's 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 for Ampere's Law.
- Students are asked to find the magnetic field using Ampere's Law for radially-varying steady current distributions inside a cylindrical shell and to make explicit symmetry arguments using Proof by Contradiction as part of their solution.
- The compare and contrast wrap-up discussion focuses on the fact that all examples have zero field inside the shell; smooth and continuous, but different answers within the shell; and look like an infinitesimally thin wire outside the shell.

### Reasons to spend class time on the activity

Informal interviews have shown that students will mimic the words “by symmetry” without really knowing what they mean. Also, they tend not to realize that the magnetic field can vary in both magnitude and direction-independently. This is a really valuable place to slowdown the pace and get students thinking about the geometry of what is going on.