JEE Main 2025 Apr 8 Shift 2, Physics Q4: Gauss's Law

JEE Main2025Apr 8, Shift 2Physics

Electric charge is transferred to an irregular metallic disk as shown in figure. If $σ_{1}$ , $σ_{2}$ , $σ_{3}$ and $σ_{4}$ are charge densities at given points then, choose the correct answer from the options given below:

(A) $σ_{1} > σ_{3}$ ; $σ_{2} = σ_{4}$

(B) $σ_{1} > σ_{2}$ ; $σ_{3} > σ_{4}$

(D) $σ_{1} < σ_{3} < σ_{2} = σ_{4}$

(E) $σ_{1} = σ_{2} = σ_{3} = σ_{4}$

A
A, B and C Only
B
A and C Only
C
D and E Only
D
B and C Only

Solution

On a charged conductor at electrostatic equilibrium, surface charge density is inversely proportional to the local radius of curvature: $σ \propto \frac{1}{ROC}$ .

From the figure, the sharp top point at $σ_{1}$ has the smallest ROC, so it carries the largest charge density.

The bottom point at $σ_{3}$ is moderately pointed with an intermediate ROC, so $σ_{3}$ lies between $σ_{1}$ and the smooth-edge densities.

The two smoothly-curved side points at $σ_{2}$ and $σ_{4}$ have equal (large) radii of curvature by symmetry, so $σ_{2} = σ_{4}$ and both are smaller than $σ_{3}$ .

Combined ordering: $σ_{1} > σ_{3} > σ_{2} = σ_{4}$ .

Statement A ( $σ_{1} > σ_{3}$ and $σ_{2} = σ_{4}$ ) is contained in this ordering, so A is true.

Statement B ( $σ_{1} > σ_{2}$ and $σ_{3} > σ_{4}$ ) is also true since $σ_{1} > σ_{2}$ and $σ_{3} > σ_{4}$ .

Statement C is the full ordering itself and is true.

Statements D and E contradict the ordering and are false.

So A, B and C are correct, matching option (1).

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JEE Main 2025 Apr 8 Shift 2, Physics Q4: Gauss's Law

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