• 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 the expectation value of energy and angular momentum as a function of time for an initial state for a particle on a ring. This state is a linear combination of energy/angular momentum eigenstates written in bra-ket notation.

In this lecture, students see a geometric derivation of the Lorentz Transformation on a spacetime diagram.

Student consider several curves on a spacetime diagram and have to judge which curves could be worldlines for an object.

• Students evaluate two given partial derivatives from a system of equations.
• Students learn/review generalized Leibniz notation.
• Students may find it helpful to use a chain rule diagram.