Electrodynamics of a magnet moving through a conducting pipe
Bibliographic record
Abstract
The popular demonstration involving a permanent magnet falling through a conducting pipe is treated as an axially symmetric boundary-value problem. Specifically, Maxwell's equations are solved for an axially symmetric magnet moving coaxially inside an infinitely long, conducting cylindrical shell of arbitrary thickness at nonrelativistic speeds. Analytic solutions for the fields are developed and used to derive the resulting drag force acting on the magnet in integral form. This treatment represents a significant improvement over existing models, which idealize the problem as a point dipole moving slowly inside a pipe of negligible thickness. It also provides a rigorous study of eddy currents under a broad range of conditions, and can be used for magnetic braking applications. The case of a uniformly magnetized cylindrical magnet is considered in detail, and a comprehensive analytical and numerical study of the properties of the drag force is presented for this geometry. Various limiting cases of interest involving the shape and speed of the magnet and the full range of conductivity and magnetic behavior of the pipe material are investigated and corresponding asymptotic formulas are developed.PACS Nos.: 81.70.Ex, 41.20.–q, 41.20.Gz
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".