• Students need to understand that the surface represents the electric potential in the center of a parallel plate capacitor. Try doing the activity Electric Potential of Two Charged Plates before this activity.
• Students should know that
  1. objects with like charge repel and opposite charge attract,
  2. object tend to move toward lower energy configurations
  3. The potential energy of a charged particle is related to its charge: \(U=qV\)
  4. The force on a charged particle is related to its charge: \(\vec{F}=q\vec{E}\)

Students calculate probabilities for a particle on a ring whose wavefunction is not easily separated into eigenstates by inspection. To find the energy, angular momentum, and position probabilities, students perform integrations with the wavefunction or decompose the wavefunction into a superposition of eigenfunctions.

The instructor gives a brief lecture about time dependence of energy eigenstates (e.g. McIntyre, 3.1). Notes for the students are attached.

In this activity, students apply the Stefan-Boltzmann equation and the principle of energy balance in steady state to find the steady state temperature of a black object in near-Earth orbit.

Students consider how changing the volume of a system changes the internal energy of the system. Students use plastic graph models to explore these functions.