论文标题
均匀加速电荷的电磁场的不连续性
A discontinuity in the electromagnetic field of a uniformly accelerated charge
论文作者
论文摘要
均匀加速电荷的电场显示了不连续的平面，该场仅在平面的一侧延伸，以有限的值在平面上突然终止。这表明无源区域中电场的非零差异意味着违反了高斯法律。为了使该场与麦克斯韦的方程无处不在，需要在不连续性平面上与$δ$功能成正比的附加字段组件。这样的“ $δ$ - 场”可能是电荷的电磁场，在无穷大加速之前，以均匀的速度接近$ c $的光速，即光速。但是，有些尝试在这种情况下得出这种$δ$场的尝试并没有完全成功。该推导的某些主张涉及精心计算，并具有一些不太明显的数学近似值。由于将得出的结果从其遵守麦克斯韦方程的限制中已经知道，并且该派生涉及统一移动电荷领域的熟悉的教科书表达式，因此人们期望一种简单，简单的方法可以导致正确的结果。在这里，从瞬时休息框架中均匀加速电荷的电磁场开始，就电荷在迟滞时间的位置和运动而言，我们以相当简单的方式得出了与Maxwell方程相一致的$δ$ field。接下来是在$δ$场中以分析方式计算能量，而不会进行任何近似值，在那里我们表明，由于电荷上的辐射反应，这种能量正是电荷会损失的能量，与其加速的变化率成正比，这是在遥远的过去所施加的。
The electric field of a uniformly accelerated charge shows a plane of discontinuity, where the field extending only on one side of the plane, terminates abruptly on the plane with a finite value. This indicates a non-zero divergence of the electric field in a source-free region, implying a violation of Gauss law. In order to make the field compliant with Maxwell's equations everywhere, an additional field component, proportional to a $δ$-function at the plane of discontinuity, is required. Such a "$δ$-field" might be the electromagnetic field of the charge, moving with a uniform velocity approaching $c$, the speed of light, prior to the imposition of acceleration at infinity. However, some attempts to derive this $δ$-field for such a case, have not been entirely successful. Some of the claims of the derivation involve elaborate calculations with some not-so-obvious mathematical approximations. Since the result to be derived is already known from the constraint of its compliance with Maxwell's equations, and the derivation involves the familiar text-book expressions for the field of a uniformly moving charge, one would expect an easy, simple approach, to lead to the correct result. Here, starting from the electromagnetic field of a uniformly accelerated charge in the instantaneous rest frame, in terms of the position and motion of the charge at the retarded time, we derive this $δ$-field, consistent with Maxwell's equations, in a fairly simple manner. This is followed by a calculation of the energy in the $δ$-field, in an analytical manner without making any approximation, where we show that this energy is exactly the one that would be lost by the charge because of the radiation reaction on the charge, proportional to its rate of change of acceleration, that was imposed on it at a distant past.
