Magnetopause and Ring-Current Extensions
r_mp(fast wind) = 9.14 R_E, between the quiet-wind (9.81 R_E) and storm-sheath (7.15 R_E) values -- closer to the quiet-wind value, since the fast wind's lower density partially offsets its higher speed in the dynamic-pressure product.
| Criterion | Points |
|---|---|
| Correct standoff-distance arithmetic | 8 |
| Correct comparative placement | 7 |
E_ring(-284 nT) = 4.38e+14 J, exactly double E_ring(-142 nT) = 2.19e+14 J -- confirming the DPS relation's exact linear (not merely approximate) dependence on Dst.
| Criterion | Points |
|---|---|
| Correct arithmetic | 8 |
| Correct exact-doubling confirmation | 7 |
A 5% increase in B0 changes E0 by a factor of 1.05^2=1.1025, i.e., a 10.2% increase in E0 -- since real secular changes in Earth's dipole field over 165 years are much smaller than 5% (of order a fraction of a percent per decade), this effect is negligible for comparing the 1859 and 2017/2024 ring-current energies at the precision used in this course.
| Criterion | Points |
|---|---|
| Correct E0 recomputation and percent-change arithmetic | 6 |
| Correct negligibility judgment for the real secular-change timescale | 4 |
P_dyn(quiet)=1.61e-09 Pa. Required pressure factor = (r_mp,quiet/6.6)^6=10.8. Required P_dyn=1.73e-08 Pa. Solving for v at fixed quiet-wind density gives v=1314 km/s -- a very high, though not physically impossible, solar wind speed, consistent with only the most extreme storm-time sheath speeds compressing the magnetopause this far inward.
| Criterion | Points |
|---|---|
| Correct pressure-factor arithmetic | 5 |
| Correct solved speed | 10 |
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Verify that the student re-derives the number for this problem's specific inputs rather than quoting a lecture example without adaptation. Watch specifically for unit-conversion errors (Gauss vs Tesla, nT vs T, km/s vs m/s, hours vs seconds), for comparative-magnitude statements given in the wrong direction, and for level-1/level-2/level-3 data-provenance conflation (e.g., presenting the order-of-magnitude flare free-energy estimate as a precise measurement, or presenting a Carrington-Dst estimate as a directly measured historical value) -- these are the most common sources of mistakes in this course.