ElectrostaticsMedium
Question
Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :
Options
A.$1:3^{1/3}$
B.$1:2^{2/3}$
C.$3^{2/3}:1$
D.$1:3^{2/3}$
Solution
Using volume conservation
$$\begin{matrix} & 3\left( \frac{4}{3}\pi r^{3} \right) = \left( \frac{4}{3}\pi R^{3} \right) \\ & R = 3^{1/3}r \\ & \frac{V_{i}}{V_{f}} = \frac{\frac{kq}{r}}{\frac{k3q}{R}} = \frac{R}{3r} = \frac{3^{1/3}r}{3r} = \frac{1}{3^{2/3}} \end{matrix}$$
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