A soap bubble (surface tension T) is charged to a maximum surface charge density σ. When the bubble is just going to burst, the radius of the bubble is given by

Engineering

Physics

Equilibrium

Surface Tension and Surface Energy

Electric Flux and Gauss Law and its Applications

Question

A soap bubble (surface tension T) is charged to a maximum surface charge density σ. When the bubble is just going to burst, the radius of the bubble is given by

$\frac{σ^{2}}{8 \in_{0} T}$

$\frac{\sqrt{8 \in_{0} T}}{σ}$

$\frac{σ}{\sqrt{8 \in_{0} T}}$

$\frac{8 \in_{0} T}{σ^{2}}$

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At equilibrium just before bursting, the excess pressure force due to surface tension is balanced by electrostatic repulsion so,

$\frac{4 T}{r} \times Area = \frac{σ^{2}}{2 \in_{0}} \times Area \Rightarrow r = \frac{8 \in_{0} T}{σ^{2}}$