Using Symmetry and Invariance to Solve Problems in Elementary Physics

Symmetry and invariance play a fundamental role in modern physics and related disciplines, and students entering a STEM field need practice with symmetry-based arguments as part of the preparation for their future careers. We refer to symmetry-based solutions as those that either make use of the existing geometric symmetry in a problem to simplify calculations or include transformations with the purpose of creating a simpler equivalent problem. We begin by giving some examples of symmetry-based solutions involving Gauss's law, where such techniques are already widely used. Then we will propose additional problems where solutions based on symmetry and invariance are appropriate, but not yet in common use to our knowledge.