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 :

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Correct answer: C. 1: 3^ 2 / 3

For three identical conducting bubbles with charge

q

and radius

r

,
Initial potential on each:

V_i = \frac{kq}{r}

When three bubbles coalesce,
Total charge

Q = 3q

and new radius from volume:

\frac{4}{3}\pi R^3 = 3 \times \frac{4}{3}\pi r^3

So

R = 3^{1/3}r

Final potential:

V_f = \frac{k(3q)}{3^{1/3}r} = \frac{3kq}{3^{1/3}r} = V_i \cdot 3^{2/3}

Ratio:

V_i : V_f = 1 : 3^{2/3}

Three small identical bubbles of water having same charge on each...

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