Potential to which a soap bubble of radius r be charged, so that pressure outside and inside same will be (take, $p_0=$ atmospheric pressure and $T=$ surface tension of soap film)

Pressure inside the soap bubble is

$p=p_0+\frac{4T}{r}$

Due to charging, electrostatic pressure is

$p_0=\frac{{\sigma }^2}{2{\epsilon }_0}$

So, net pressure inside the charged bubble is

$p_0+\frac{4T}{r}-\frac{{\sigma }^2}{2{\epsilon }_0}$

By given condition,

$$\begin{gathered} p_0+\frac{4T}{r}-\frac{{\sigma }^2}{2{\epsilon }_0}=p_0 \\ \frac{4T}{r}=\frac{{\sigma }^2}{2{\in }_0}=\frac{{\epsilon }_0{V}^2}{2r^2} \\ V=\sqrt{\frac{8Tr}{{\epsilon }_0}} \end{gathered}$$