Use of a varying turn-density coil (VTDC) to generate a constant-gradient magnetic field and to demonstrate the magnetic force on a permanent magnet
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Bibliographic record
Abstract
In this study, we proposed that a constant gradient magnetic field could be generated by the construction of a current-carrying coil possessing a turn-density (number of turns per unit length) that varies linearly with axial position (i.e., a varying turn-density coil, VTDC). A VTDC is easily constructed and could be used to demonstrate how a ferromagnet placed in a magnetic field experiences a net force. Using the Biot–Savart law, we predicted that a ferromagnetic dipole suspended in a VTDC experiences a force proportional to the length of the dipole. We designed and executed an experiment to test our prediction. A coil with a turn-density varying at a rate of 0.11 cm −2 was constructed. Rare-earth magnets were suspended along the centre of the VTDC using a string that was attached to a mass resting on a scale. The scale reading measured the force experienced by the hanging magnet. The procedures were also carried out in a constant turn-density solenoid (control). A direct linear relationship between force and magnet length was observed in the VTDC, whereas no force was detected in the zero-gradient field solenoid (p < 0.000 001). Linear regressions suggested that the observed data matched the predicted values (95% certainty). The magnetic moment of 0.56 ± 0.21 J/T is in reasonable agreement with remnant magnetization for neodymium magnets of ∼1 T. We found that our easily-built VTDC produced a uniform gradient as no significant differences were observed when magnets were hung at different axial positions. Overall, the results were supportive of the theory. Our VTDC could be readily constructed and used in a physics classroom to demonstrate basic principles of electromagnetism.
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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