• assignment Current in a Wire

assignment Homework

##### Current in a Wire
Static Fields 2022 (3 years) The current density in a cylindrical wire of radius $R$ is given by $\vec{J}(\vec{r})=\alpha s^3\cos^2\phi\,\hat{z}$. Find the total current in the wire.
• group Establish Classroom Norms

group Small Group Activity

60 min.

##### Establish Classroom Norms
Theoretical Mechanics 2021 (2 years)

In this hour-long activity, students establish classroom norms for being respectful when working in small groups. This is particularly helpful in the first course a cohort of students encounters.
• assignment Symmetry Arguments for Gauss's Law

assignment Homework

##### Symmetry Arguments for Gauss's Law
Static Fields 2022 (4 years)

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.

• group Systems of Equations Compare and Contrast

group Small Group Activity

60 min.

##### Systems of Equations Compare and Contrast
• group Name the experiment

group Small Group Activity

30 min.

##### Name the experiment
Energy and Entropy 2021 (3 years)

Student groups design an experiment that measures an assigned partial derivative. In a compare-and-contrast wrap-up, groups report on how they would measure their derivatives.
• face Central Forces Introduction: Lecture Notes

face Lecture

5 min.

##### Central Forces Introduction: Lecture Notes
Central Forces 2022
• assignment Derivatives from Data (NIST)

assignment Homework

##### Derivatives from Data (NIST)
Energy and Entropy 2021 (2 years) Use the NIST web site “Thermophysical Properties of Fluid Systems” to answer the following questions. This site is an excellent resource for finding experimentally measured properties of fluids.
1. Find the partial derivatives $\left(\frac{\partial {S}}{\partial {T}}\right)_{p}$ $\left(\frac{\partial {S}}{\partial {T}}\right)_{V}$ where $p$ is the pressure, $V$ is the volume, $S$ is the entropy, and $T$ is the temperature. Please find these derivatives for one gram of methanol at one atmosphere of pressure and at room temperature.
2. Why does it take only two variables to define the state?
3. Why are the derivatives above different?
4. What do the words isobaric, isothermal, and isochoric mean?
• group Total Charge

group Small Group Activity

30 min.

##### Total Charge
Static Fields 2022 (4 years)

Integration Sequence

In this small group activity, students integrate over non-uniform charge densities in cylindrical and spherical coordinates to calculate total charge.
• computer Approximating Functions with Power Series

computer Computer Simulation

30 min.

##### Approximating Functions with Power Series
Static Fields 2022 (8 years)

Power Series Sequence (E&M)

Students use prepared Sage code or a prepared Mathematica notebook to plot $\sin\theta$ simultaneously with several terms of a power series expansion to judge how well the approximation fits. Students can alter the worksheet to change the number of terms in the expansion and even to change the function that is being considered. Students should have already calculated the coefficients for the power series expansion in a previous activity, Calculating Coefficients for a Power Series.
• group Electric Field Due to a Ring of Charge

group Small Group Activity

30 min.

##### Electric Field Due to a Ring of Charge
Static Fields 2022 (6 years)

Power Series Sequence (E&M)

Ring Cycle Sequence

Students work in groups of three 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.

• AIMS Maxwell 2021 (2 years)

Task: Draw a right triangle. Put a circle around the right angle, that is, the angle that is $\frac\pi2$ radians.

• Complete the assignment using your choice of technology. You may write your answers on paper, write them electronically (for instance using xournal), or typeset them (for instance using LaTeX).
• If using software, please export to PDF. If writing by hand, please scan your work using the AIMS scanner if possible. You can also use a scanning app; Gradescope offers advice and suggested apps at this URL. The preferred format is PDF; photos or JPEG scans are less easy to read (and much larger), and should be used only if no alternative is available.)
• Please make sure that your file name includes your own name and the number of the assignment, such as "Tevian2.pdf."

Using Gradescope: We will arrange for you to have a Gradescope account, after which you should receive access instructions directly from them. To submit an assignment: