Question

If 27 charged water droplets, each of radius $10^{-6~\text{m}$ and charge $10^{-12}~\text{C}$ coalesce to form a single spherical drop, then the potential of the big drop is}

• A. $9~\text{V}$
• B. $27~\text{V}$
• C. $39~\text{V}$
• D. $81~\text{V}$

Hint:

For coalescing drops, radius becomes $rN^{1/3}$ and charge adds linearly.

Answer 1

The Correct Option is D

New radius: $R = r \cdot N^{1/3} = 10^{-6} \cdot 3 = 3 \times 10^{-6}~\text{m}$
Total charge: $Q = 27 \cdot 10^{-12} = 27 \times 10^{-12}~\text{C}$
Potential $V = \dfrac{1}{4\pi\varepsilon_0} \cdot \dfrac{Q}{R}$
$= 9 \times 10^9 \cdot \dfrac{27 \times 10^{-12}}{3 \times 10^{-6}} = 81~\text{V}$