Question

A thin circular disc of radius R is uniformly charged with surface charge density $\sigma$. Find the electric potential at a point located on the rim (corner) of the disc.

Answer 1

Infinite

Answer 2

The potential at a point on the rim of a uniformly charged disc is calculated by integrating the contributions from infinitesimal charge elements. By considering concentric rings, the potential integral involves $\int_{0}^{2\pi} \frac{d\theta}{\sqrt{R^2 - 2Rx\cos\theta + x^2}}$. As the radius $x$ of the ring approaches the disc radius $R$, the denominator approaches $2R|\sin(\theta/2)|$. The integral $\int_{0}^{2\pi} \frac{d\theta}{|\sin(\theta/2)|}$ diverges, indicating an infinite potential contribution from charges near the point on the rim.