GATE 2017 EE (EE2) – Question 65

Electromagnetic Fields · Effect of dielectric medium, Capacitance of simple configurations · 2 marks · Numerical answer

A thin soap bubble has R=1 cm, thickness a=3.3 μm (a≪R) and potential 1 V relative to infinity. It bursts into one spherical drop containing all the soap. The volumes are $4\pi R^2a$ for the thin shell and $4\pi r^3/3$ for the drop. Find the drop potential in volts to two decimals.

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Correct answer: 9.50 to 10.50

Explanation

Conservation of soap volume gives $r^3=3R^2a$. With R=0.01 m and a=$3.3\times10^{-6}$ m, r≈0.000996655 m.

For an isolated charged sphere, $V=Q/(4\pi\epsilon_0r)$. Conserved charge therefore makes potential inversely proportional to radius. The new potential is $1\cdot R/r\approx10.0336$ V.

Rounded to two decimals, this is **10.03 V**, within 9.50–10.50 V. The charge-conservation idealization assumes no charge loss during bursting.

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