Question

Two metallic shells \(A\) and \(B\) of radii \(3\,\text{cm}\) and \(4\,\text{cm}\) are given electric charges \(20\,\mu\text{C}\) and \(40\,\mu\text{C}\) respectively. If the shells are arranged concentrically, then the ratio of the surface charge densities of the shells \(A\) and \(B\) is

• A. \(4:27\)
• B. \(4:3\)
• C. \(16:9\)
• D. \(16:27\)

Hint:

For concentric conducting shells, - the induced charge on the inner surface of the outer shell equals the negative of the charge enclosed, - the remaining charge resides on the outer surface. Also, \[ \boxed{ \sigma=\frac{Q}{4\pi R^2}. } \]

Answer 1

The Correct Option is D