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A soap bubble of radius \( 3 \mathrm{cm} \) is charged with surface charge density \( \sigma \) such that \( \frac{\sigma^{2}}{\epsilon_{0}}=0.4 S I \) units. The excess pressure inside the bubble in SI unit (surface tension of soap solution \( =3 \times \) \( 10^{-3} \mathrm{N} / \mathrm{m} \) ) is:

1. \( 0 . \)
2. 0.2
3. 0.5
4. 0.25

Correct answer: 0.25

Solution

A soap bubble has excess pressure from two sources: surface tension on its two surfaces and electrostatic repulsion of the surface charge. Using the given data, the total comes out to 0.25 Pa in SI units.

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