A short improvisational role-playing skit based on the Star Trek series in which students explore the definition and notation for position vectors, the importance of choosing an origin, and the geometric nature of the distance formula.
\[\vert\vec{r}-\vec{r}^\prime\vert=\sqrt{(x-x^\prime)^2+(y-y^\prime)^2-(z-z^\prime)^2}\]

Consider the finite line with a uniform charge density from class.

Write an integral expression for the electric field at any point in space due
to the finite line. In addition to your usual physics sense-making, you must
include a clearly labeled figure and discuss what happens to the direction of
the unit vectors as you integrate.Consider the finite line with a uniform
charge density from class.

Perform the integral to find the \(z\)-component of the electric field. In
addition to your usual physics sense-making, you must compare your result to
the gradient of the electric potential we found in class. (If you want to
challenge yourself, do the \(s\)-component as well!)

For an infinitesimally thin cylindrical shell of radius \(b\) with uniform surface
charge density \(\sigma\), the electric field is zero for \(s<b\) and \(\vec{E}=
\frac{\sigma b}{\epsilon_0 s}\, \hat s\) for \(s > b\). Use the differential form
of Gauss' Law to find the charge density everywhere in space.

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 a Parallel Plate Capacitor” before this activity.

Students should know that

objects with like charge repel and opposite charge attract,

object tend to move toward lower energy configurations

The potential energy of a charged particle is related to its charge: \(U=qV\)

The force on a charged particle is related to its charge: \(\vec{F}=q\vec{E}\)