Electric charge is transferred to an irregular metallic disk as shown in figure. If $$\sigma_1$$, $$\sigma_2$$, $$\sigma_3$$ and $$\sigma_4$$ are charge densities at given points then, 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) $$\sigma_1 = \sigma_2 = \sigma_3 = \sigma_4$$

(E) $$\sigma_1 = \sigma_2 > \sigma_3 = \sigma_4$$

The surface charge density at any point on a conductor is inversely proportional to its local radius of curvature ($$R$$): $$\sigma \propto \frac{1}{R}$$

$$\sigma_1$$ is located at the sharpest point (pointed tip) at the top. This region has the absolute smallest radius of curvature ($$R_1$$).

$$\sigma_3$$ is located at the curved base at the bottom, which has a distinct curvature but is less sharp than the tip ($$R_3 > R_1$$).

$$\sigma_2$$ and $$\sigma_4$$ are situated on the symmetrical side flanks, which are relatively flat and identical in curvature ($$R_2 = R_4 > R_3 > R_1$$).

$$\sigma_1 > \sigma_3 > \sigma_2 = \sigma_4$$