Question

Two spherical hollow spheres of radii '\(R_1\)' and '\(R_2\)' are charged with same charge. Let '\(σ_1\)' and '\(σ_2\)' are their respective charge densities, then the ratio \(σ_1\) to \(σ_2\) is

• A. \(R_1:R_2\)
• B. \(R_2:R_1\)
• C. \(R_2^2:R_1^2\)
• D. \(R_1^2:R_2^2\)

Hint:

Surface charge density is charge divided by surface area.

Answer 1

The Correct Option is C

Step 1: Inverse proportion
For the same charge, the density is inversely proportional to the area, which goes as $R^2$. So the smaller sphere has the larger density. Option (C).

Final Answer:
R2^2 : R1^2. \[ \boxed{\text{(C)}\ R_2^2:R_1^2} \]