Question

Three metallic spherical shells (not concentric) of radii R, 2R and 4R are given charges \(Q_{1}\), \(Q_{2}\) and \(Q_{3}\) respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges \(Q_{1}:Q_{2}:Q_{3}\), is

• A. \(1:2:4\)
• B. \(1:3:9\)
• C. \(1:4:16\)
• D. \(1:6:12\)

Hint:

The shells are far apart, so each charge sits on its own outer surface. Charge equals surface density times area.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The shells are not concentric and far apart, so each charge sits entirely on its own outer surface.

Step 2: Calculation
\(Q=\sigma\,4\pi r^{2}\). With equal \(\sigma\), \(Q\propto r^{2}\).

Step 3: Ratio
Radii are \(R:2R:4R\), so \(Q_{1}:Q_{2}:Q_{3}=1:4:16\).

Final Answer:
The charge ratio is 1:4:16. \[ \boxed{\text{(C) }1:4:16} \]