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---
## 让运动与静态基准保持同一比较构型
磁力问题从一个明确变化开始：保持电荷量和参考横向分离不变，使两个电荷获得共同运动。设 $q_1,q_2$ 以同一恒定速度 $\mathbf v$ 平行运动，二者连线与速度垂直；速度相对于局域均匀空间背景定义。参考分离为 $r>0$，$\hat{\mathbf r}$ 从 $q_1$ 指向 $q_2$，$\beta=v/c$、$\gamma=(1-\beta^2)^{-1/2}$。
[库仑页](/theory/electromagnetism/coulomb-interaction)已经固定核外逆平方构成律、源强和力的方向。本页沿用忽略有限尺寸、外部梯度及边界修正的条件。$\mathbf F_0$ 是同电荷量、同参考距离的静态基准，$\mathbf F_T$ 是与真值物理位移配对的实际作用；$F_0,F_T$ 在下面的大小公式中为非负值。
## 横向距离怎样进入逆平方作用
LVE 给出 $K(\phi)=\gamma(1-\beta\cos\phi)$。在横向 $\phi=\pi/2$ 上，$K=\gamma$，故：
接下来调用第三章的构成输入：真值距离 $r_T$ 是库仑作用实际发生的距离。代入 $F_T=|q_1q_2|/(4\pi\varepsilon_0r_T^2)$，分母成为 $4\pi\varepsilon_0\gamma^2r^2$；把静态基准提出，再用恒等式 $\gamma^{-2}=1-\beta^2$，得到：
运动作用仍沿两电荷连线，改变的是强度。对带符号矢量取同一基准的差额：
这就是 ASD 在给定构型内组织磁作用的方式。$\Delta\mathbf F_m$ 是总作用相对静态基准的修正，$\mathbf F_T$ 才是总力。若已经用 $r_T$ 计算了总作用，再另加一次这个差额，就会重复计算同一尺度效应。
同号电荷的 $\mathbf F_0$ 向外，修正向内，因此排斥减小；异号电荷的 $\mathbf F_0$ 向内，修正向外，因此吸引大小减小。用正的减少量描述两种情况时，另记：
$F_m^{\mathrm{red}}$ 是大小之差，不能用它取代带方向的 $\Delta\mathbf F_m$。采用 SI 电磁归一化 $\varepsilon_0\mu_0=c^{-2}$，同一差额还可写为：
这里 $\mu_0$ 是真空磁导率。这一步改写单位归一化，没有另加一条独立基本磁力定律。$\varepsilon_0,\mu_0$ 的微观来源也未由这个乘积关系确定。
## 为什么这里不需要低速截断
距离关系使用完整 $\gamma$，代入后使用的是精确恒等式。因此差额恰与 $\beta^2$ 成正比；说它是二阶项，不表示从更长级数中舍去了高阶项。结论适用于这一构成律及共同恒速、平行、横向分离构型的全部 $0\leq v
图中比较同号电荷的归一化作用，长度和箭头仅示意构型。滑动速度可以检验上述代数关系，不提供实验数据。后续矢势页采用低速近区近似，不会反向把本页的特殊构型结果变成低速截断。
## 同一虚功中的真值力和坐标广义力
实验比较需要先说明力与什么位移配对。固定共同速度，真值距离 $r_T=\gamma r$ 的虚变分满足 $dr_T=\gamma\,dr$。相互作用势能 $U_T=q_1q_2/(4\pi\varepsilon_0r_T)$ 在两种变量中的虚功为：
这组虚功式中的 $F_T,F_0,F_r$ 可以采用沿 $\hat{\mathbf r}$ 的带符号分量；讨论同号电荷时其数值也就是上述大小。$F_T=-\partial U_T/\partial r_T$ 与真值位移配对，$F_r=-\partial U_T(\gamma r)/\partial r$ 与参考坐标位移配对。链式法则给出 $F_r=\gamma F_T$，而非产生第二个物理相互作用。
第二章把力接到机械动量变化率与功—能关系。应用时，物理位移、机械动量和过程参数要在同一表示中对应；参考坐标广义力则与该坐标的共轭动量配对。轨迹曲率、束团动量交换、支撑的机械反作用或电光信号，都还需要各自的装置映射。不能把仪器示值未经计算就认作 $F_T$ 或 $F_r$。变速时还要保留尺度因子的速度依赖和伴随场能量交换。
## 同构型比较为什么要保留量定义
现在单独引入标准 Maxwell–Lorentz 电动力学作为比较对象。对同号电荷的相同共同速度、横向分离，它给出的实验室电力、正的磁减少量和总横向力为：
这些关系没有被用作前面的 ASD 推导前提。ASD 真值力为 $F_0/\gamma^2$，坐标广义力为 $F_0/\gamma$；后者与标准实验室总力数值重合，所配对的变量却不同。低速展开进一步显示：
磁减少量的低速主系数相同，不等于总受力在同阶上相同：标准电场的速度修正也进入总力。ASD 后面的准静态势和最小耦合再现这一磁主项，不能据此宣称已经完成一般源耦合与真值总力的对应。实验上是否出现差异，需要让两种模型计算同一装置、同一读数及同一计量过程。[实验矩阵](/tests/electromagnetism)和[高速区分量任务](/open-problems/electromagnetism/high-gamma-discriminator)保留这一要求。
## 推导依赖与来源
依据第三章第一节，式（3.1）—（3.10）。代数链在所列几何和构成输入内闭合；一般两源问题及仪器映射不由这一构型自动解决。