论文标题
无穷大的边缘：边缘效应与无穷大假设之间的冲突，用于在导电板上电荷分布
Edge of Infinity: The Clash between Edge Effect and Infinity Assumption for the Distribution of Charge on a Conducting Plate
论文作者
论文摘要
我们重新审查了入门物理课程中给出的一个熟悉的问题，即确定与平行于相同大小的均匀带电的介电板时，在未充电的``无限大大''导电板上确定诱导的电荷分布。我们表明，无论板有多大，边缘效应始终都足够强，可以影响中央区域深处的电荷分布，这完全破坏了无穷大假设（两侧的表面电荷密度均匀，相反的幅度）。为了进行更详细的分析，我们解决了托有方程式在二维空间中的类似设置，并获得确切的电荷分布，从而帮助我们了解了在中央，渐近线和边缘区域中电荷分布的情况。
We re-examine a familiar problem given in introductory physics courses, about determining the induced charge distribution on an uncharged ``infinitely-large'' conducting plate when placing parallel to it a uniform charged dielectric plate of the same size. We show that, no matter how large the plates are, the edge effect will always be strong enough to influence the charge distribution deep in the central region, which totally destroyed the infinity assumption (that the surface charge densities on the two sides are uniform and of opposite magnitudes). For a more detailed analysis, we solve Poisson's equation for a similar setting in two-dimensional space and obtain the exact charge distribution, helping us to understand what happens how charge distributes at the central, the asymptotic, and the edge regions.
