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27 identical drops are charged to 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be ______ V.

Asked in JEE Main 25th June 2nd Shift 2022 · Coalescing charged drops

Answer: 198

Step-by-step solution

Conserving volume, R=n^1/3r=27^1/3r=3r; conserving charge, Q=27q.

V_big=(kQ)/R=(k(27q))/(3r)=9·(kq)/r, i.e. V_big=n^2/3Vₛₘₐₗₗ.

n^2/3=27^2/3=9.

V_big=9×22=198 V.

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