Electrostatics

JEE Main level, single correct, medium

155 of 311

Question 155 of 311

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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Answer: (C) 1:32/31: 3^{2 / 3}

For three identical conducting bubbles with charge qq and radius rr,
Initial potential on each: Vi=kqrV_i = \frac{kq}{r}
When three bubbles coalesce,
Total charge Q=3qQ = 3q and new radius from volume: 43πR3=3×43πr3\frac{4}{3}\pi R^3 = 3 \times \frac{4}{3}\pi r^3
So R=31/3rR = 3^{1/3}r
Final potential: Vf=k(3q)31/3r=3kq31/3r=Vi⋅32/3V_f = \frac{k(3q)}{3^{1/3}r} = \frac{3kq}{3^{1/3}r} = V_i \cdot 3^{2/3}
Ratio: Vi:Vf=1:32/3V_i : V_f = 1 : 3^{2/3}

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