Analytical Calculation of the Magnetic Vector Potential of an Axisymmetric Solenoid in the Presence of Iron Parts
Bibliographic record
Abstract
This paper presents an analytical calculation method for the computation of the magnetic vector potential of an axisymmetric solenoid in the presence of an iron shield and a ferromagnetic core. The proposed method can be used as a fast analytical computation technique for accelerating the design optimization process of the solenoid systems. In this paper, the analysis of the current carrying coil in the presence of the ferromagnetic materials is treated as a boundary value problem. The solution approach is based on partitioning the solution domain into distinct regions. The general form of the solution to Maxwell's equation in each region along with the corresponding boundary conditions is obtained using the Fourier analysis and the separation of variables. The final solution to the boundary value problem is constituted by considering the continuity of the magnetic vector potential, as well as the magnetic field, on the interfaces between the regions. Finally, the proposed analytical computation method is applied on an electromagnetic actuator. The magnetic vector potential is computed over the entire solution domain, and the result is compared with that of the finite-element method.
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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 | 0.001 |
| 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".