Bonus
Note to players: Pencil and paper may be helpful. The Gaussian pillbox is used to find the E-field on an infinite sheet with a uniform “surface” version of this quantity, denoted sigma. For 10 points each:
[10m] Name this quantity whose “volume” form is proportional to the E-field’s divergence.
ANSWER: charge density [accept surface charge density or volume charge density; reject “charge”; reject “density”]
[10e] The Gaussian pillbox is usually visualized either as a rectangular prism or as this shape, which has volume pi r-squared h.
ANSWER: cylinder [accept cylindrical coordinates]
[10h] [Read slowly] If an infinite plane in a vacuum has positive surface charge density sigma, this is the resulting uniform magnitude of the electric field everywhere, which changes sign at the plane. This value can be found by using a Gaussian pillbox and noting that the field is normal to the plane. You have 10 seconds and must answer in SI units.
ANSWER: sigma over 2 epsilon-naught [or 1/2 sigma over epsilon-naught; accept divided by in place of “over”; accept permittivity of free space or epsilon-zero in place of “epsilon-naught”] (A pillbox covering an area A of the plane contains a charge of sigma-A; the total electric flux passing through the ends of the pillbox is AE − A(−E) = 2AE; by Gauss’s law, sigma-A/epsilon-naught = 2AE, so E is sigma over 2 epsilon-naught.)
<Physics>
Answerlines and category may not exactly match the version played at all sites
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Cornell A | North Carolina A | 10 | 10 | 10 | 30 | MEH |
Summary
| Tournament | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|
| 2025 ACF Nationals | Yes | 1 | 30.00 | 100% | 100% | 100% |