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JEE Main 2023 (12 Apr, Shift 1) · Electric Potential & Equipotentials

Electric Potential & Equipotentials question from JEE Main 2023 (12 Apr, Shift 1)

Q60JEE Main 2023 · 12 APR · SHIFT 1Easy

Electric Potential & Equipotentials

64 identical drops each charged upto potential of $10\text{ mV}$ are combined to form a bigger drop. The potential of the bigger drop will be __________ $\text{mV}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 160

Charge is conserved: $Q = nq$ ; volume is conserved: $\frac{4}{3}\pi R^3 = n\cdot\frac{4}{3}\pi r^3 \Rightarrow R = n^{1/3}r$
$V' = \frac{kQ}{R} = \frac{knq}{n^{1/3}r} = n^{2/3}V$
$V' = 64^{2/3}\times 10 = 16 \times 10 = 160\text{ mV}$
So the answer is 160 mV.

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