Question

An isolated and charged spherical soap bubble has a radius $r$ and the pressure outside is atmospheric. If $T$ is the surface tension of soap solution, then charge on drop is

• A. $2\sqrt{\frac{2rT}{{\epsilon }_0}}$
• B. $8\pi r\sqrt{2rT{\epsilon }_0}$
• C. $8\pi r\sqrt{rT{\epsilon }_0}$
• D. $8\pi r\sqrt{\frac{2rT}{{\epsilon }_0}}$

Answer 1

The correct option is B $8\pi r\sqrt{2rT{\epsilon }_0}$

Inside pressure must be $\frac{4T}{r}$ greater than outside pressure for bubble. This excess pressure is provided by charge on bubble.

$\frac{4T}{r}=\frac{{\sigma }^2}{2{\epsilon }_0}\frac{4T}{r}=\frac{Q^2}{16{\pi }^2{r}^4\times 2{\epsilon }_0}[\sigma =\frac{Q}{4\pi r^2}]Q=8\pi r\sqrt{2rT{\epsilon }_0}$