VALIDITY CHECK OF MUTUAL INDUCTANCE FORMULAS FOR CIRCULAR FILAMENTS WITH LATERAL AND ANGULAR MISALIGNMENTS
Bibliographic record
Abstract
In this paper we derived the formula for calculating the mutual inductance between circular fllaments with lateral and angular misalignment by using the approach of the magnetic vector potential. The results obtained correspond to those of F. W. Grover, although the latter used the general formula given by the Neumann integral instead of a vector potential approach. However, the major purpose of this paper is to clarify some confusion introduced in previous works regarding the mutual inductance calculation between thin fllamentary circular coils with parallel axes in air. This problem has been solved by Kim etal. (8) using the magnetic vector potential, but unfortunately it leads to erroneous results, even for slight misalignments of the coils' center axes. This is why we chose to use the approach of the magnetic vector potential to show that, when properly derived, the results must indeed reduce to the well known F. W. Grover's formulas.
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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 | 0.001 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".