Question

In air, a charged soap bubble of radius 'r' is in equilibrium having outside and inside pressures being equal. The charge on the bubble is ______.

($ϵ=$ permittivity of free space, T=surface tension of soap solution).

• A. $4\pi r^2\sqrt{\frac{2T{ϵ}_0}{r}}$
• B. $4\pi r^2\sqrt{\frac{4T{ϵ}_0}{r}}$
• C. $4\pi r^2\sqrt{\frac{6T{ϵ}_0}{r}}$
• D. $4\pi r^2\sqrt{\frac{8T{ϵ}_0}{r}}$

Answer 1

The correct option is D $4\pi r^2\sqrt{\frac{8T{ϵ}_0}{r}}$

In the given scenario, the excess pressure due to surface tension must balance the electrostatic pressure. Note that the surface tension force tries to collapse the bubble whereas the electrostatic pressure tries to expand it.

$\frac{4T}{r}=\frac{{\sigma }^2}{2{ϵ}_0}\Rightarrow \sigma =\sqrt{\frac{8T{ϵ}_0}{r}}$

$\Rightarrow Q=4\pi r^2\sigma =4\pi r^2\sqrt{\frac{8T{ϵ}_0}{r}}$

(Surface charge density = total surface charge/total surface area on which it is distributed)