Electric charge is transferred to an irregular metallic disk as shown in the figure. If $\sigma_1$, $\sigma_2$, $\sigma_3$ and $\sigma_4$ are the charge densities at the given points, choose the correct answer from the options given below:
(A) $\sigma_1 > \sigma_3$; $\sigma_2 = \sigma_4$
(B) $\sigma_1 > \sigma_2$; $\sigma_3 > \sigma_4$
(C) $\sigma_1 > \sigma_3 > \sigma_2 = \sigma_4$
(D) $\sigma_1 < \sigma_3 < \sigma_2 = \sigma_4$
(E) $\sigma_1 = \sigma_2 = \sigma_3 = \sigma_4$
Answer: (A) A, B and C only
On a charged conductor the surface charge density is larger where the surface is more sharply curved (smaller radius of curvature).
The top point (1) is the sharpest, the bottom point (3) is less sharp, and the two side points (2 and 4) are equally and least curved:
$$\sigma_1 > \sigma_3 > \sigma_2 = \sigma_4$$
This makes (A), (B) and (C) true, and (D) and (E) false.
Solution by Sreeraj P, M.Sc Physics