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: Compare the options
Equal surface charge density means charge grows with surface area, which goes as the square of the radius.

Step 2: Why the other options fail
1:2:4 is proportional to radius, and 1:3:9 and 1:6:12 do not match $1^{2}:2^{2}:4^{2}$.

Step 3: Final answer
Charges scale as $r^{2}$, giving 1:4:16.

Final Answer:
Charges scale as $r^{2}$, giving 1:4:16. \[ \boxed{\text{(C) }1:4:16} \]