Electric charge is transferred to an irregular metallic disk as shown in the figure. If σ₁, σ₂, σ₃ and σ₄ are charge densities at given points then, choose the correct answer from the options given below:
A. σ₁>σ₃ ; σ₂=σ₄
B. σ₁>σ₂ ; σ₃>σ₄
C. σ₁>σ₃>σ₂=σ₄
D. σ₁<σ₃<σ₂=σ₄
E. σ₁=σ₂=σ₃=σ₄

Solution

Physics sir · 3 steps

On a conductor, sharper means denser: the pointier the spot, the more charge piles up there.

1. The rule. A charged conductor is at one potential everywhere. To keep it so, surface charge density is largest where the surface curves most sharply, roughly σ ∝ 1/r, with r the local radius of curvature.

   Point	Shape there	Radius of curvature	Charge density
   σ₁ (top)	sharpest tip	smallest	largest
   σ₃ (bottom)	blunter point	larger than at top	second largest
   σ₂, σ₄ (sides)	same smooth round arc	largest, and equal	smallest, and equal

2. Check each statement. This gives σ₁ > σ₃ > σ₂ = σ₄, so C is true. A follows from it directly. B is also true, since σ₁ > σ₂ and σ₃ > σ₄. D reverses the order and E ignores the shape, so both are false.
3. So. Statements A, B and C are correct, which is option (d).

The idea to keep. On any charged conductor, look at how sharply the surface bends. Smaller radius of curvature means higher charge density. That is why lightning conductors are pointed.

Answer from the NTA final answer key. Solution by PrepWiser.