Self-torque and angular momentum balance for a spinning charged sphere
Bibliographic record
Abstract
Angular momentum balance is examined in the context of the electrodynamics of a spinning charged sphere, which is allowed to possess any variable angular velocity. We calculate the electric and magnetic fields of the (hollow) sphere, and express them as expansions in powers of τ/tc ≪ 1, the ratio of the light-travel time τ across the sphere and the characteristic time scale tc of variation of the angular velocity. From the fields we compute the self-torque exerted by the fields on the sphere, and argue that only a piece of this self-torque can be associated with radiation reaction. Then we obtain the rate at which angular momentum is radiated away by the shell, and the total angular momentum contained in the electromagnetic field. With these results we demonstrate explicitly that the field angular momentum is lost in part to radiation and in part to the self-torque; angular momentum balance is thereby established. Finally, we examine the angular motion of the sphere under the combined action of the self-torque and an additional torque supplied by an external agent.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".