Physics · Application of surface tension: drops, bubbles and capillary rise
A soap bubble of radius is charged with surface charge density such that units.
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:
- A. \( 0 . \)
- B. 0.2
- C. 0.5
- D. 0.25
Step-by-step solution
For a soap bubble, excess pressure due to surface tension is ΔP_s = 4T/R = 4×3×10⁻³/0.03 = 0.4 Pa. Electrostatic pressure due to charge is ΔP_e = σ²/(2ε₀) = (0.4)/2 = 0.2 Pa outward. Net excess pressure inside = ΔP_s - ΔP_e = 0.4 - 0.2 = 0.2 Pa.
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