accessibility_new Kinesthetic
5 min.
Special Relativity Time Dilation Light Clock Kinesthetic Activity
Students act out the classic light clock scenario for deriving time dilation.group Small Group Activity
30 min.
coulomb's law electric field charge ring symmetry integral power series superposition
Students work in small groups to use Coulomb's Law \[\vec{E}(\vec{r}) =\frac{1}{4\pi\epsilon_0}\int\frac{\rho(\vec{r}^{\,\prime})\left(\vec{r}-\vec{r}^{\,\prime}\right)}{\vert \vec{r}-\vec{r}^{\,\prime}\vert^3} \, d\tau^{\prime}\] to find an integral expression for the electric field, \(\vec{E}(\vec{r})\), everywhere in space, due to a ring of charge.
In an optional extension, students find a series expansion for \(\vec{E}(\vec{r})\) either on the axis or in the plane of the ring, for either small or large values of the relevant geometric variable. Add an extra half hour or more to the time estimate for the optional extension.
group Small Group Activity
120 min.
assignment Homework
The gravitational field due to a spherical shell of matter (or equivalently, the
electric field due to a spherical shell of charge) is given by:
\begin{equation}
\vec g =
\begin{cases}
0&\textrm{for } r<a\\
-G \,\frac{M}{b^3-a^3}\,
\left( r-\frac{a^3}{r^2}\right)\, \hat r & \textrm{for } a<r<b\\
-G\,\frac{M}{r^2}\, \hat r & \textrm{for } r>b \\
\end{cases}
\end{equation}
This problem explores the consequences of the divergence theorem for this shell.
group Small Group Activity
30 min.
assignment Homework
group Small Group Activity
30 min.
group Small Group Activity
30 min.
group Small Group Activity
30 min.
Instructions for 2022: You will need to complete this assignment in a 15 minute appointment on Zoom or in person with one of the members of the teaching team between 1/21 and 10 pm on 1/26. Here is a link to a sign-up page.
You are required to watch a sample video for how to make symmetry arguments here. As demonstrated in the video you should bring with you to the meeting a cylinder, an observer, and a vector.
Use good symmetry arguments to find the possible direction for the electric field due to a charged wire. Also, use good symmetry arguments to find the possible functional dependence of the electric field due to a charged wire. Rather than writing this up to turn in, you should find a member of the teaching team and make the arguments to them verbally.