Curl field of a continuous current

Obtained by taking the curl of the effective current potential; the microscopic wire force does not follow from the common-velocity pair law alone.

Theory · EFFECTIVE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 3

ASD-WEB-EM-027

\mathbf B(\mathbf r)=\frac{\mu_0}{4\pi}\int\frac{\mathbf J(\mathbf r')\times\mathbf R}{R^3}\,d^3r',\quad\mathbf R=\mathbf r-\mathbf r'

Obtained by taking the curl of the effective current potential; the microscopic wire force does not follow from the common-velocity pair law alone.
Chapter reference: Final collected manuscript · Chapter 3, equations (3.28), (3.29) · ASD-BOOK-ddbade997b45

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ASD-WEB-EM-027 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

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Final collected manuscript · Chapter 3, equations (3.28), (3.29)

Obtained by taking the curl of the effective current potential; the microscopic wire force does not follow from the common-velocity pair law alone.

Conditions retained in this adoption

Special two-body result: uniform exterior background, equal parallel velocities, transverse separation and virtual displacement at fixed velocity.
Free Maxwell representation: long waves, weak perturbations, transverse constraint, constant coefficients and normalization.
Minimal-coupling sources: macroscopic coarse graining, low-speed point sources or a low-frequency near zone; high-speed closed sources require separate construction.

Specific unresolved source issues

Local results do not automatically close high-speed topological sources, full instrument mapping or global directed propagation.

Source locators: p1002 · p1015 · p1044 · p1046 · p1048 · p1053 · p1058 · p1063 · p1067 · p1073 · p1075 · p1080 · p1085 · p1090 · p1096 · p1128 · p1153 · p1154 · p1155 · 最终合订稿 · 第三章式 (3.28)、(3.29)

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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EM-f06476f55cae · 第三章 / Chapter 3 · (3.28)–(3.29), PDF p. 8

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