Question

64 identical spheres each having charge q coalesce to form one big sphere. Find the ratio of the surface charge density of the big sphere to that of small sphere

Hint:

For $n$ coalescing identical drops, general relations are:
Radius: $R = n^{1/3}r$
Charge: $Q = nq$
Potential: $V = n^{2/3}v$
Surface charge density: $\sigma_{\text{big}} = n^{1/3} \sigma_{\text{small}}$ (Here $64^{1/3} = 4$).

Answer 1