title, topic, keyword
Small group, whiteboard, etc
Required in-class time for activities
Leave blank to search both

Activities

Small Group Activity

30 min.

##### Grey space capsule
In this small group activity, students work out the steady state temperature of an object absorbing and emitting blackbody radiation.
• Found in: Contemporary Challenges course(s)

Small Group Activity

30 min.

##### Black space capsule
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.
• Found in: Contemporary Challenges course(s)

Problem

##### Heat shields
A black (nonreflective) sheet of metal at high temperature $T_h$ is parallel to a cold black sheet of metal at temperature $T_c$. Each sheet has an area $A$ which is much greater than the distance between them. The sheets are in vacuum, so energy can only be transferred by radiation.
1. Solve for the net power transferred between the two sheets.

2. A third black metal sheet is inserted between the other two and is allowed to come to a steady state temperature $T_m$. Find the temperature of the middle sheet, and solve for the new net power transferred between the hot and cold sheets. This is the principle of the heat shield, and is part of how the James Web telescope shield works.
3. Optional: Find the power through an $N$-layer sandwich.

• Found in: Thermal and Statistical Physics course(s)

Small Group Activity

10 min.

##### Thermal radiation at twice the temperature
This small group activity has students reasoning about how the Planck distribution shifts when the temperature is doubled. This leads to a qualitative argument for the Stefan-Boltzmann law.
• Found in: Contemporary Challenges course(s)

Lecture

120 min.

##### Boltzmann probabilities and Helmholtz
These notes, from the third week of https://paradigms.oregonstate.edu/courses/ph441 cover the canonical ensemble and Helmholtz free energy. They include a number of small group activities.
• Found in: Thermal and Statistical Physics course(s)

Problem

##### Boltzmann probabilities
Consider a three-state system with energies $(-\epsilon,0,\epsilon)$.
1. At infinite temperature, what are the probabilities of the three states being occupied? What is the internal energy $U$? What is the entropy $S$?
2. At very low temperature, what are the three probabilities?
3. What are the three probabilities at zero temperature? What is the internal energy $U$? What is the entropy $S$?
4. What happens to the probabilities if you allow the temperature to be negative?
• Found in: Energy and Entropy, Thermal and Statistical Physics course(s)

Problem

##### Energy fluctuations
Consider a system of fixed volume in thermal contact with a resevoir. Show that the mean square fluctuations in the energy of the system is $$\left<\left(\varepsilon-\langle\varepsilon\rangle\right)^2\right> = k_BT^2\left(\frac{\partial U}{\partial T}\right)_{V}$$ Here $U$ is the conventional symbol for $\langle\varepsilon\rangle$. Hint: Use the partition function $Z$ to relate $\left(\frac{\partial U}{\partial T}\right)_V$ to the mean square fluctuation. Also, multiply out the term $(\cdots)^2$.
• Found in: Thermal and Statistical Physics course(s)

Problem

##### Gauss's Law for a Rod inside a Cube
Consider a thin charged rod of length $L$ standing along the $z$-axis with the bottom end on the $x,y$-plane. The charge density $\lambda_0$ is constant. Find the total flux of the electric field through a closed cubical surface with sides of length $3L$ centered at the origin.
• Found in: AIMS Maxwell, Static Fields, Problem-Solving course(s)

Problem

##### Symmetry Arguments for Gauss's Law

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.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s)

Problem

5 min.

##### Find Force Law: Logarithmic Spiral Orbit

(Use the equation for orbit shape.) Gain experience with unusual force laws.

In science fiction movies, characters often talk about a spaceship “spiralling in” right before it hits the planet. But all orbits in a $1/r^2$ force are conic sections, not spirals. This spiralling in happens because the spaceship hits atmosphere and the drag from the atmosphere changes the shape of the orbit. But, in an alternate universe, we might have other force laws.

In class, we discussed how to calculate the shape of the orbit for an inverse square potential. More generally, the equation for the orbit of a mass $\mu$ under the influence of a central force $f(r)$ is given by: \begin{align} \frac{d^2 u}{d\phi^2} + u &=-\frac{\mu}{\ell^2}\frac{1}{u^2}f\left(\frac{1}{u}\right)\\ \Rightarrow f\left(\frac{1}{u}\right)&=-\frac{\ell^2}{\mu}u^2 \left(\frac{d^2 u}{d\phi^2} + u\right) \end{align} where $u=r^{-1}$.

Find the force law for a mass $\mu$, under the influence of a central-force field, that moves in a logarithmic spiral orbit given by $r = ke^{\alpha \phi}$, where $k$ and $\alpha$ are constants.

• Found in: Central Forces course(s)

Problem

5 min.

##### Line Sources Using Coulomb's Law
1. (4pts) Find the electric field around a finite, uniformly charged, straight rod, at a point a distance $s$ straight out from the midpoint, starting from Coulomb's Law.
2. (4pts) Find the electric field around an infinite, uniformly charged, straight rod, starting from the result for a finite rod.
• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s)

Problem

##### Differential Form of Gauss's Law

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.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s)

Problem

5 min.

##### Bottle in a Bottle

The internal energy of helium gas at temperature $T$ is to a very good approximation given by \begin{align} U &= \frac32 Nk_BT \end{align}

Consider a very irreversible process in which a small bottle of helium is placed inside a large bottle, which otherwise contains vacuum. The inner bottle contains a slow leak, so that the helium leaks into the outer bottle. The inner bottle contains one tenth the volume of the outer bottle, which is insulated. What is the change in temperature when this process is complete? How much of the helium will remain in the small bottle?

• Found in: Energy and Entropy course(s)

Small White Board Question

5 min.

##### Newton's 2nd Law SWBQ

Write Newton's 2nd Law for a single mass.

## Notes:

LG 2024: I added the Euler-Lagrange equation as an example of a generalized statement of Newton's 2nd Law. I'm planning on using a Lagrangian approach for the 2-body problem.

• Found in: Central Forces course(s)

Small Group Activity

60 min.

##### The Wire
Students compute a vector line integral, then investigate whether this integral is path independent.
• Found in: Vector Calculus II, Surfaces/Bridge Workshop, Problem-Solving course(s) Found in: Workshop Presentations 2023 sequence(s)

Small Group Activity

30 min.

##### Name the experiment (changing entropy)
Students are placed into small groups and asked to create an experimental setup they can use to measure the partial derivative they are given, in which entropy changes.
• Found in: Energy and Entropy course(s) Found in: Name the experiment sequence(s)

Small Group Activity

60 min.

##### Electrostatic Potential Due to a Pair of Charges (with Series)
Students work in small groups to use the superposition principle $V(\vec{r}) = \frac{1}{4\pi\epsilon_0}\sum_i \frac{q_i}{\vert\vec{r}-\vec{r}_i\vert}$ to find the electrostatic potential $V$ everywhere in space due to a pair of charges (either identical charges or a dipole). Different groups are assigned different arrangements of charges and different regions of space to consider: either on the axis of the charges or in the plane equidistant from the two charges, for either small or large values of the relevant geometric variable. Each group is asked to find a power series expansion for the electrostatic potential, valid in their group's assigned region of space. The whole class wrap-up discussion then compares and contrasts the results and discuss the symmetries of the two cases.
• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s) Found in: Power Series Sequence (E&M), E&M Ring Cycle Sequence sequence(s)

Lecture

5 min.

##### Wavelength of peak intensity
This very short lecture introduces Wein's displacement law.
• Found in: Contemporary Challenges course(s)

Small Group Activity

30 min.

##### Changes in Internal Energy
Students consider the change in internal energy during three different processes involving a container of water vapor on a stove. Using the 1st Law of Thermodynamics, students reason about how the internal energy would change and then compare this prediction with data from NIST presented as a contour plot.
• Found in: Warm-Up sequence(s)

Small Group Activity

120 min.

##### Projectile with Linear Drag
Students consider projectile motion of an object that experiences drag force that in linear with the velocity. Students consider the horizontal motion and the vertical motion separately. Students solve Newton's 2nd law as a differential equation.
• Found in: Theoretical Mechanics course(s) Found in: Drag Force Sequence, Separable ODE's Sequence sequence(s)

Small Group Activity

30 min.

##### Using $pV$ and $TS$ Plots
Students work out heat and work for rectangular paths on $pV$ and $TS$ plots. This gives with computing heat and work, applying the First Law, and recognizing that internal energy is a state function, which cannot change after a cyclic process.
• Found in: Energy and Entropy course(s)

Small Group Activity

30 min.

##### Electric Field Due to a Ring of Charge

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.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s) Found in: Power Series Sequence (E&M), E&M Ring Cycle Sequence sequence(s)

Small Group Activity

30 min.

##### Magnetic Field Due to a Spinning Ring of Charge

Students work in small groups to use the Biot-Savart law $\vec{B}(\vec{r}) =\frac{\mu_0}{4\pi}\int\frac{\vec{J}(\vec{r}^{\,\prime})\times \left(\vec{r}-\vec{r}^{\,\prime}\right)}{\vert \vec{r}-\vec{r}^{\,\prime}\vert^3} \, d\tau^{\prime}$ to find an integral expression for the magnetic field, $\vec{B}(\vec{r})$, due to a spinning ring of charge.

In an optional extension, students find a series expansion for $\vec{B}(\vec{r})$ 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.

• Found in: Static Fields, AIMS Maxwell, Problem-Solving course(s) Found in: Power Series Sequence (E&M), E&M Ring Cycle Sequence sequence(s)

Computational Activity

120 min.

##### Electrostatic potential of spherical shell
Students solve numerically for the potential due to a spherical shell of charge. Although this potential is straightforward to compute using Gauss's Law, it serves as a nice example for numerically integrating in spherical coordinates because the correct answer is easy to recognize.
• Found in: Computational Physics Lab II course(s) Found in: Computational integrating charge distributions sequence(s)