Question

A soap bubble of radius $1.0$ cm is electrically charged so that the pressure inside the bubble is identical with the outside pressure. If the surface tension of the soap solution is $0.028$ N /m, the electric charge on the bubble will be:

• A. $6.08\times {10}^{-8}C$
• B. $5.31\times {10}^{-8}C$
• C. $3.04\times {10}^{-8}C$
• D. $1.77\times {10}^{-8}C$

Answer 1

The correct option is D $1.77\times {10}^{-8}C$

The net pressure inside the bubble is $P-4T/R+{\sigma }^2/2{ϵ}_0$ where $P$ is the outside pressure. This inside pressure is identical to outside pressure.Therefore,
${\sigma }^2/2{ϵ}_0=4T/R$
$\sigma \times 4\pi R^2=Q$
$Q^2=8T{ϵ}_0\times 16{\pi }^2\times R^3=3.131\times {10}^{-16}$

$Q=1.77\times {10}^{-8}C$