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. $R=\frac{{\sigma }^2}{8{\epsilon }_{0}T}$
• B. $R=8{\epsilon }_0\frac{T}{{\sigma }^2}$
• C. $R=\frac{\sigma }{\sqrt{8{\epsilon }_{0}T}}$
• D. $R=\frac{\sqrt{8{\epsilon }_{0}T}}{\sigma }$

Answer 1

Answer: (B)

The pressure due to surface tension $=\frac{4T}{R}$
The pressure due to electrostatic forces $=\frac{{\sigma }^2}{2{\epsilon }_0}$
Just before the bubble bursts.
$\frac{4T}{R}=\frac{{\sigma }^2}{2{\epsilon }_0}$ or $R=\frac{8T{\epsilon }_0}{{\sigma }^2}$