JEE Main 2026 Jan 22 Shift 2, Physics Q5: Electric Potential

JEE Main2026Jan 22, Shift 2Physics

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 :

A
$1 : 3^{1/3}$
B
$1 : 2^{2/3}$
C
$3^{2/3} : 1$
D
$1 : 3^{2/3}$

Solution

Volume conservation: $3 \cdot \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3} \Rightarrow R = 3^{1/3} r$ .

Charge conservation: each small bubble carries charge $q$ , so the big bubble has charge $3 q$ .

Potentials: $V_{i} = \frac{k q}{r}$ , $V_{f} = \frac{k \cdot 3 q}{R} = \frac{3 k q}{3 ^{1/3} r} = \frac{3 ^{2/3} k q}{r}$ .

Ratio $\frac{V _{i}}{V _{f}} = \frac{1}{3 ^{2/3}}$ , i.e., $1 : 3^{2/3}$ .

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JEE Main 2026 Jan 22 Shift 2, Physics Q5: Electric Potential

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