There are two metallic spheres A and B having radii equal to R and 2R respectively. A charge Q is distributed on these two spheres such that the two spheres have equal surface charge densities. The ratio of charge on A to charge on B is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 : 4
The surface charge density is the charge per unit area, \( \sigma = q/(4\pi r^{2}) \) for a sphere of radius r. Equal densities on the two spheres means the charges are in the ratio of their surface areas.
\( \displaystyle \sigma_A = \sigma_B \Rightarrow \frac{q_A}{4\pi R^{2}} = \frac{q_B}{4\pi (2R)^{2}} \)
\( \displaystyle \frac{q_A}{q_B} = \frac{R^{2}}{(2R)^{2}} = \frac{1}{4} \)