Question #43779

This question tests the student's ability to distinguish between the electric field of a point charge (which follows an inverse-square law) and that of an infinite sheet (which is constant).

A common lethal mistake is assuming the potential energy takes the form $U \propto 1/r$ or attempting to integrate a variable force, often by incorrectly modeling the sheet's effective charge as a finite disc $Q = \sigma \pi d^2$.

This leads to the incorrect application of $V = \frac{Q}{4\pi\varepsilon_0 d}$, resulting in the trap answer $\sqrt{\frac{e\sigma d}{m\varepsilon_0}}$.

The correct approach requires recognizing the constant nature of the field $E = \sigma / (2\varepsilon_0)$ and applying the Work-Energy Theorem for a constant force.