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. $Q=8\pi r\sqrt{rT{ϵ}_0}$
• B. $Q=8\pi r\sqrt{2rT{ϵ}_0}$
• C. $Q=4\pi r\sqrt{2rT{ϵ}_0}$
• D. $Q=4\pi r\sqrt{rT{ϵ}_0}$

Answer 1

Answer: (B)

The excess pressure inside a soap bubble due to surface tension is $\frac{4T}{r}$ .
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.
$\frac{4T}{r}=\frac{{\sigma }^2}{2{ϵ}_0}$
$\Rightarrow \frac{4T}{r}=\frac{1}{2{\left(ϵ\right)}_0}{\left(\frac{Q}{4\pi r^2}\right)}^2\Rightarrow Q=8\pi r\sqrt{2rT{\left(ϵ\right)}_0}$