Electric charge is transferred to an irregular metallic disk as shown… | JEE Main 2025 (8 Apr, Shift 2)

Q26JEE Main 2025 · 8 APR · SHIFT 2Easy

Electric Flux & Gauss's Law

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 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. $\sigma_1 < \sigma_3 < \sigma_2 = \sigma_4$

E. $\sigma_1 = \sigma_2 = \sigma_3 = \sigma_4$

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Answer: (d)

On a conductor, surface charge density is larger where the radius of curvature is smaller: $\sigma \propto \frac{1}{r}$ .
The pointed top (1) has the smallest radius, the lower tip (3) is sharper than the round sides, and points 2 and 4 are symmetric.
So $\sigma_1 > \sigma_3 > \sigma_2 = \sigma_4$ : C is true, hence A ( $\sigma_1 > \sigma_3$ , $\sigma_2 = \sigma_4$ ) and B ( $\sigma_1 > \sigma_2$ , $\sigma_3 > \sigma_4$ ) are true.
D and E are false, so the answer is (d) A, B and C only.

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