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If n identical water drops assumed spherical each charged to a potential difference U coalesce to a single drop, the potential energy of the single drop is (assume that drops are uniformly charged):plzz explain n^(1/3) U n^(2/3) U n^(4/3) U n^(5/3)U

If n identical water drops assumed spherical each charged to a potential difference U coalesce to a single drop,  the potential energy of the single drop is (assume that drops are uniformly charged):plzz explain
  1. n^(1/3) U
  2. n^(2/3) U
  3. n^(4/3) U
  4. n^(5/3)U

Grade:

2 Answers

Arun
25763 Points
2 years ago
Let potential f 1 drop = Kq/r =U

Volume of n drops = volume of bigger drop 

n  4/3 pi (r)^3  = 4/3 pi (R)^3

Therefore ,  R = ( (n)^1/3) r 

also charge remains conserved 

charge on 1 drop = q 

charge on big drop containing n drops = (nq) 

Therefore potential on big drop = K (nq)/ ((n)^1/3)r

Mithilesh kumar
15 Points
16 days ago
U=qV=kqQ/r    Also 4/3 pi R3 =4/3 pi r3 n so, R=n1/3 r
U’=knqnQ/R=kn2qQ/n1/3r=n5/3U
hence, potential energy of the bigger drop is n5/3 times the potential energy of the smaller one.

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