If "n" identical drops each of potential "v" combine to form a larger drop
of potential "V". Prove that V= v *{n^(2/3)}
I wonder how such impossible derivation can be proved

Hi binayakafle

The larger drop will have n times the initial volume and charge. Now, can you find that "impossible" formula?

Hi songoku. I just solved this problem for my upcoming exam. Thanks for your help.
I may add that you have to assume that the drops are spherical. At least I reached the result assuming this. I'm not sure if the result holds for non spherical drops, although I'd love to know!

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Isaac
If the problem is too hard just let the Universe solve it.

Hi Arbolis

Yes we assume that the drops are spherical. I am also not sure if the result holds for non spherical drops, maybe Pmb or physicsquest can help us

As I'm very weak in mathematics,so please post 2 or 3 steps of solution of that problem. I'd b grateful

Hi binayakafle

Let :
1 = smaller drop
2 = larger drop

*The larger drop will have n times the initial charge ---> Q2 = n Q1 ...... (a)
*The larger drop will have n times the initial volume ---> r2 = (something) r1 ..... (b)

find that "something" then substitute it to the equation for V (electric potential)