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Quasistatic transverse source response

u is constant under spatial differentiation; this is not a general all-speed moving-charge field.

Theory · EFFECTIVE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 3

ASD-WEB-EM-019
B≃1c2∇Φstatic×u=1c2u×Estatic\mathbf B\simeq\frac1{c^2}\nabla\Phi_{\rm static}\times\mathbf u=\frac1{c^2}\mathbf u\times\mathbf E_{\rm static}

u is constant under spatial differentiation; this is not a general all-speed moving-charge field.
Chapter reference: Final collected manuscript · Chapter 3, equations (3.16) · ASD-BOOK-ddbade997b45

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ASD-WEB-EM-019 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 (3.16)

u is constant under spatial differentiation; this is not a general all-speed moving-charge field.

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 (3.16)

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

EM-f06476f55cae · 第三章 / Chapter 3 · (3.16), PDF p. 5

DEPENDS ON

Dependencies

algebraQuasistatic potential of a slow sourceASD-WEB-EM-018inputPotential representation of the fieldsASD-WEB-EM-016
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Uses of this equation

Subsequent equationTwo-velocity structure in the slow-source effective modelASD-WEB-EM-023DocumentMagnetic Field: Spatial Curl and Material Response
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