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 $X \pi r \sqrt{2 r T \varepsilon_0}$ then find the value of $X$.

• A. 8
• B. 9
• C. 7
• D. 2

Answer 1

Answer: (A)

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

This excess pressure is provided by charge on bubble.
$\frac{4 T }{ r }=\frac{\sigma^2}{2 \varepsilon_0} ; \frac{4 T }{ r }=\frac{ Q ^2}{16 \pi^2 r ^4 \times 2 \varepsilon_0}\left[\sigma=\frac{ Q }{4 \pi r ^2}\right]$
$Q =8 \pi r \sqrt{2 rT \varepsilon_0}$