Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble.

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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 :

Accepted Answer

Using volume conservation$$\begin{matrix} & 3\left( \frac{4}{3}\pi r^{3} ight) = \left( \frac{4}{3}\pi R^{3} ight) \ & R = 3^{1/3}r \ & \frac{V_{i}}{V_{f}} = \frac{\frac{kq}{r}}{\frac{k3q}{R}} = \frac{R}{3r} = \frac{3^{1/3}r}{3r} = \frac{1}{3^{2/3}} \end{matrix}$$

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