Question

An isolated and charged spherical soap bubble has a radius $r$ and the pressure inside is atmospheric. If $T$ is the surface tension of soap solution, then charge on drop is $X\pi r\sqrt{2rT{\epsilon }_0}$ then find the value of $X$.

• A. 8
• B. 9
• C. 7
• D. 2

Answer 1

Answer: (A)

Inside pressure must be $\frac{4T}{r}$ greater than outside pressure in bubble.

This excess pressure is provided by charge on bubble.
$\frac{4T}{r}=\frac{{\sigma }^2}{2{\epsilon }_0};\frac{4T}{r}=\frac{Q^2}{16{\pi }^2{r}^4\times 2{\epsilon }_0}\left[\sigma =\frac{Q}{4\pi r^2}\right]$
$Q=8\pi r\sqrt{2rT{\epsilon }_0}$