Oersted field¶

Physical problem¶

This page is the public physical and authoring contract for the interaction. It separates authored semantics, planner resolution, executable backend lanes, and scientific qualification.

Governing equations¶

Solved-current field¶

Charge transport supplies signed conventional current \(\mathbf J_c\) satisfying continuity. A direct Biot–Savart realization is

There is no \(\mu_0\) in this expression for \(\mathbf H\); \(\mathbf B_{\mathrm{oe}}=\mu_0\mathbf H_{\mathrm{oe}}\) in vacuum. A vector-potential realization solves a compatible \(H(\mathrm{curl})\) problem and computes \(\mathbf B=\nabla\times\mathbf A\).

A local two-electrode current bar is not automatically a globally closed source for general Oersted evaluation. Closure identity, mesh, orientation, revisions, and accepted current view are part of the physical contract.

Symbols and SI units¶

Capability matrices¶

Python API and stage-first example¶

# %% Study, execution lane, and magnetic body
import fullmag as fm

nm = 1.0e-9
study = fm.study("oersted_cylinder_reference")
study.engine("fdm")
study.device("cpu", precision="double")
study.mode("strict")
study.objects.mesh.defaults(cell_size=(2 * nm, 2 * nm, 2 * nm))
body = study.geometry(fm.Box(40 * nm, 20 * nm, 4 * nm), name="film")
body.Ms = 8.0e5
body.Aex = 13.0e-12
body.alpha = 0.02
body.m = fm.texture.uniform(1.0, 0.0, 0.0)

study.exchange()
study.oersted(fm.OerstedCylinder(current=5.0e-3, radius=20 * nm, axis=(0.0, 0.0, 1.0)))
study.stages.add_run(stage_id="sample", until=1.0e-12)

ProblemIR¶

The analytic and solved-current families use distinct tagged records. The minimal canonical fragments are shown in the Python section above; resolved method, closure identity, current-view revision, solver, device, precision, and mesh belong to planner/runtime provenance.

Validation boundary and required code corrections¶

OerstedCylinder currently converts current, center, and axis without complete finite, non-zero, or unit-axis validation at construction. Harden the constructor: current must be finite, radius finite and positive, center finite, and axis finite/non-zero then normalized once.

OerstedField has no public OE-F1/OE-F2 method parameter. Documentation must not imply that the user selected a method when the planner selected it internally. Source maps referring to worktree-uncommitted tests or an older immutable commit must be regenerated for the audited revision.

Required numerical validation¶

• analytic radial profile inside/outside the cylinder and continuity at \(R\);

• right-hand-rule sign under current and axis reversal;

• zero field on the axis;

• direct-current scaling and envelope timing;

• Biot–Savart comparison with analytic wire/loop geometries;

• current-balance and circuit-closure residuals;

• OE-F1 quadrature and OE-F2 airbox/mesh convergence;

• \(\nabla\cdot\mathbf B=0\) and compatible projection checks;

• strict rejection of stale current identity and unsupported GPU requests.

Limitations and recommended split¶

Create separate pages: analytic-cylinder.md, solved-current.md, external-lead-closure.md, and vector-potential.md. The root should compare them and expose the capability matrix. Do not mark the family globally implemented while the solved-current public path is mainly semantic/bounded.

Scientific bibliography¶

1. J. D. Jackson, Classical Electrodynamics, 3rd ed., Wiley, 1998.

2. P. Monk, Finite Element Methods for Maxwell’s Equations, Oxford University Press, 2003.

Control Room crosswalk¶

This is a navigation page; the selected interaction or foundation is configured by its linked Python API and object/stage editor. The category itself has no standalone control. frontend support is not implemented applies to physical parameters without a matching control. See {doc}/frontend/capability-register; do not infer UI support from backend or Python availability.

Python/API crosswalk¶

The linked Python API page is authoritative for exact functions, arguments, units, and failure semantics. If this page is a foundation or category overview, runnable Python is ot applicable here and must be taken from the terminal API page.

Bibliography and source scope¶

Use the scientific bibliography and source-code index on the linked terminal page. This block adds no new equation or unverified implementation claim.

Round-trip and failure semantics¶

Requested intent preserves the authored model, coefficients, orientations, targets, and execution request. Resolved execution records the selected solver, device, precision, discretization, and capability decision. Validation errors reject malformed or contradictory data before runtime. Unsupported combinations fail closed and are not silently omitted or converted to another interaction.

Assumptions and validity¶

The authored model is valid only within the continuum, discretization, boundary, and capability limits stated on this page.

Implementation mapping¶

Python owns authoring and serialization, ProblemIR owns canonical intent, planners own legality and realization selection, and backend kernels own numerical evaluation.

Source-code index¶