Magnetic Force Between Inclined Circular Filaments Placed in Any Desired Position
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Bibliographic record
Abstract
This paper presents new general formulas for calculating the magnetic force between inclined circular filaments placed in any desired position. We use two approaches to calculate the magnetic force, one based on Biot-Savart law and another based on the mutual inductance between these coils. All mathematical procedures are completely described to define coil positions that lead to relatively easy method for calculating the magnetic force between inclined circular filaments in any desired position. Two formulas obtained by the simple integration of different expressions in terms of complete elliptic integrals of the first and second kind give the same numerical results. The presented methods are understandable, numerically suitable and easy applicable for engineers and physicists. We validated the new formulas through a series of examples, which are presented here.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it