## Activity: Grey space capsule

Contemporary Challenges 2022 (4 years)
In this small group activity, students work out the steady state temperature of an object absorbing and emitting blackbody radiation.
• Media

This activity follows Using the Stefan-Boltzmann law

A grey space capsule is sent on a trip to the Moon. The surface is designed to reflect 50% of the incident sunlight (i.e. it is “grey” for wavelengths less than about 3 or 4 $\mu\text{m}$). The total intensity of radiation emitted by the surface (wavelengths longer than about 3 or 4 $\mu\text{m}$) are still described by $\sigma T^4$.

The capsule is spherical and has a radius of 3 meters.

The space capsule reaches thermal equilibrium after being bathed in sunlight for a few hours. The capsule is rotating and is made of thermally conducting metal, so that all sides have the same temperature. Find the temperature.

• group Black space capsule

group Small Group Activity

30 min.

##### Black space capsule
Contemporary Challenges 2022 (3 years)

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.
• assignment Surface temperature of the Earth

assignment Homework

##### Surface temperature of the Earth
Temperature Radiation Thermal and Statistical Physics 2020 Calculate the temperature of the surface of the Earth on the assumption that as a black body in thermal equilibrium it reradiates as much thermal radiation as it receives from the Sun. Assume also that the surface of the Earth is a constant temperature over the day-night cycle. Use the sun's surface temperature $T_{\odot}=5800\text{K}$; and the sun's radius $R_{\odot}=7\times 10^{10}\text{cm}$; and the Earth-Sun distance of $1.5\times 10^{13}\text{cm}$.
• assignment Magnetic Field and Current

assignment Homework

##### Magnetic Field and Current
Static Fields 2023 (4 years) Consider the magnetic field $\vec{B}(s,\phi,z)= \begin{cases} 0&0\le s<a\\ \alpha \frac{1}{s}(s^4-a^4)\, \hat{\phi}&a<s<b\\ 0&s>b \end{cases}$
1. Use step and/or delta functions to write this magnetic field as a single expression valid everywhere in space.
2. Find a formula for the current density that creates this magnetic field.
3. Interpret your formula for the current density, i.e. explain briefly in words where the current is.
• assignment Current in a Wire

assignment Homework

##### Current in a Wire
Static Fields 2023 (4 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.
• assignment Current from a Spinning Cylinder

assignment Homework

##### Current from a Spinning Cylinder
A solid cylinder with radius $R$ and height $H$ has its base on the $x,y$-plane and is symmetric around the $z$-axis. There is a fixed volume charge density on the cylinder $\rho=\alpha z$. If the cylinder is spinning with period $T$:
1. Find the volume current density.
2. Find the total current.
• accessibility_new Acting Out Current Density

accessibility_new Kinesthetic

10 min.

##### Acting Out Current Density
Static Fields 2023 (6 years)

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 Static Fields Equation Sheet

group Small Group Activity

5 min.

##### Static Fields Equation Sheet
Static Fields 2023 (5 years)

Learning Outcomes