INTRODUCING FICTITIOUS CURRENTS FOR CALCU- LATING ANALYTICALLY THE ELECTRIC FIELD IN CYLINDRICAL CAPACITORS
Bibliographic record
Abstract
Abstract—The aim of this paper is to show the interest of using equivalence models for calculating the electric field produced by cylindrical capacitors with dielectrics. To do so, we use an equivalent model, based on the dual Maxwell’s Equations for calculating the two electric field components created inside the capacitor and outside it. This equivalent model uses fictitious currents generating a electric vector potential that allows us to determine the electric field components in all points in space. The electric field produced by charge distributions as capacitor with dielectrics is generally determined by using the coulombian model. Indeed, it is well known that the electric field derives from a scalar potential. By using the Maxwell’s equations, this scalar potential is in fact linked to the existence of charge distributions that are generally located on the faces of the capacitors. However, this last model does not allow us to obtain reduced analytical expressions since it involves the calculation of charge volume density appearing in the dielectric material for arcshaped cylindrical topologies. Consequently, it is interesting to look for another approach that gives analytical expressions with a lower computational cost. In this paper, we show that the use of fictitious currents instead of charges allow us to obtain 3D analytical reduced expressions with a lower computational cost. This analytical approach is compared to the coulombian model for showing the equivalence between the two approaches.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".