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JEE Main 2022 (30 Jun, Shift 1) · Electrostatic Potential Energy

Electrostatic Potential Energy question from JEE Main 2022 (30 Jun, Shift 1)

Q44JEE Main 2022 · 30 JUN · SHIFT 1Medium

Electrostatic Potential Energy

Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be ____________ E. Where E is the potential energy of a single smaller drop.

Numerical answer type. Work it out, then open the answer.

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Answer: 32

Self-energy of a sphere: $U = \frac{kQ^2}{2R}$ , so $U \propto \frac{Q^2}{R}$ .
8 drops: $R = 2r$ , $Q = 8q$ .
$\frac{U_{big}}{E} = \frac{64}{2} = 32$
So the big drop has energy $32E$ .

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