Edge of Infinity: The Clash between Edge Effect and Infinity Assumption for the Distribution of Charge on a Conducting Plate
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.