Question

An isolated soap bubble is kept in a container in which the pressure is maintained at $P_{0}$ . The bubble is given some charge due to which its radius increases to $r$ and the pressure inside the bubble reduces to $P_{0}$ . If the surface tension of the soap bubble is $T$ , then the charge given to the bubble is

• A. $Q=8\pi r\sqrt{r T \epsilon _{0}}$
• B. $Q=8\pi r\sqrt{2 r T \epsilon _{0}}$
• C. $Q=4\pi r\sqrt{2 r T \epsilon _{0}}$
• D. $Q=4\pi r\sqrt{r T \epsilon _{0}}$

Answer 1

Answer: (B)

The excess pressure inside a soap bubble due to surface tension is $\frac{4 T}{r}$ .
In the given problem the pressure of the air inside and outside the bubble is the same, hence the excess pressure in this situation should be due to the electrostatic pressure.
$\frac{4 T}{r}=\frac{\sigma ^{2}}{2 \epsilon _{0}}$
$\Rightarrow \frac{4 T}{r}=\frac{1}{2 \left(\epsilon \right)_{0}}\left(\frac{Q}{4 \pi r^{2}}\right)^{2}\Rightarrow Q=8\pi r\sqrt{2 r T \left(\epsilon \right)_{0}}$