accessibility_new Kinesthetic

10 min.

Acting Out Charge Densities

Static Fields 2023 (7 years)

density charge density mass density linear density uniform idealization

Integration Sequence

Ring Cycle Sequence

Students, pretending they are point charges, move around the room acting out various prompts from the instructor regarding charge densities, including linear \(\lambda\), surface \(\sigma\), and volume \(\rho\) charge densities, both uniform and non-uniform. The instructor demonstrates what it means to measure these quantities. In a remote setting, we have students manipulate 10 coins to model the prompts in this activity and the we demonstrate the answers with coins under a doc cam.

accessibility_new Kinesthetic

10 min.

Acting Out Current Density

Static Fields 2023 (6 years)

Steady current current density magnetic field idealization

Integration Sequence

Ring Cycle Sequence

Students, pretending they are point charges, move around the room so as to make an imaginary magnetic field meter register a constant magnetic field, introducing the concept of steady current. Students act out linear \(\vec{I}\), surface \(\vec{K}\), and volume \(\vec{J}\) current densities. The instructor demonstrates what it means to measure these quantities by counting how many students pass through a gate.

group Small Group Activity

10 min.

Proportional Reasoning

Static Fields 2023 (3 years) In this small group activity, students calculate a (linear) function to represent the charge density on a one-dimensional rod from a description of the charge density in words.

group Small Group Activity

30 min.

Electric Field Due to a Ring of Charge

Static Fields 2023 (8 years)

coulomb's law electric field charge ring symmetry integral power series superposition

Power Series Sequence (E&M)

Ring Cycle Sequence

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

30 min.

Magnetic Vector Potential Due to a Spinning Charged Ring

Static Fields 2023 (6 years)

compare and contrast mathematica magnetic vector potential magnetic fields vector field symmetry

Power Series Sequence (E&M)

Ring Cycle Sequence

Students work in small groups to use the superposition principle \[\vec{A}(\vec{r}) =\frac{\mu_0}{4\pi}\int\frac{\vec{J}(\vec{r}^{\,\prime})}{\vert \vec{r}-\vec{r}^{\,\prime}\vert}\, d\tau^{\prime}\] to find an integral expression for the magnetic vector potential, \(\vec{A}(\vec{r})\), due to a spinning ring of charge.

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

30 min.

A glass of water

Energy and Entropy 2021 (2 years)

thermodynamics intensive extensive temperature volume energy entropy

Students generate a list of properties a glass of water might have. The class then discusses and categorizes those properties.

group Small Group Activity

30 min.

Electric Potential of Two Charged Plates

Students examine a plastic "surface" graph of the electric potential due to two charged plates (near the center of the plates) and explore the properties of the electric potential.

group Small Group Activity

30 min.

Electrostatic Potential Due to a Ring of Charge

Static Fields 2023 (8 years)

electrostatic potential charge linear charge density taylor series power series scalar field superposition symmetry distance formula

Power Series Sequence (E&M)

Warm-Up

Ring Cycle Sequence

Students work in small groups to use the superposition principle \[V(\vec{r}) =\frac{1}{4\pi\epsilon_0}\int\frac{\rho(\vec{r}^{\,\prime})}{\vert \vec{r}-\vec{r}^{\,\prime}\vert} \, d\tau^{\prime}\] to find an integral expression for the electrostatic potential, \(V(\vec{r})\), everywhere in space, due to a ring of charge.

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

keyboard Computational Activity

120 min.

Mean position

Computational Physics Lab II 2023 (2 years)

probability density particle in a box wave function quantum mechanics

Students compute probabilities and averages given a probability density in one dimension. This activity serves as a soft introduction to the particle in a box, introducing all the concepts that are needed.

group Small Group Activity

30 min.

Magnetic Field Due to a Spinning Ring of Charge

Static Fields 2023 (7 years)

magnetic fields current Biot-Savart law vector field symmetry

Power Series Sequence (E&M)

Ring Cycle Sequence

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.

face Lecture

120 min.

Ideal Gas

Thermal and Statistical Physics 2020

ideal gas particle in a box grand canonical ensemble chemical potential statistical mechanics

These notes from week 6 of Thermal and Statistical Physics cover the ideal gas from a grand canonical standpoint starting with the solutions to a particle in a three-dimensional box. They include a number of small group activities.