Question

A soap bubble (surface tension $= T$) is charged to a maximum surface, density of charge $= \sigma$ When it is just going to burst? Its radius $R$ is given by

• A. $R =\frac{ \sigma^2}{8 \varepsilon_0 T}$
• B. $R = 8\,\varepsilon_0 \frac{T}{\sigma^2}$
• C. $R =\frac{\sigma}{\sqrt{8 \varepsilon_{0}T}}$
• D. $R =\frac{\sqrt{8 \varepsilon_{0}T}}{\sigma}$

Answer 1

Answer: (B)

The pressure due to surface tension $= \frac{4T}{R}$
The pressure due to electrostatic forces $ = \frac{\sigma^2}{2 \varepsilon_0}$
Just before the bubble bursts.
$\frac{4T}{R} = \frac{\sigma^2}{2 \,\varepsilon_0}$ or $R = \frac{8 T \varepsilon_0}{\sigma^2}$