Question

In air, a charged soap bubble of radius ‘$r$’ is in equilibrium having outside and inside pressures being equal. The charge on the drop is ($\varepsilon_0 =$ permittivity of free space, $T =$ surface tension of soap solution)

• A. $4\pi r^{2}\sqrt{\frac{2T\varepsilon_{0}}{r}}$
• B. $4\pi r^{2}\sqrt{\frac{4T\varepsilon_{0}}{r}}$
• C. $4\pi r^{2}\sqrt{\frac{6T\varepsilon_{0}}{r}}$
• D. $4\pi r^{2}\sqrt{\frac{8T\varepsilon_{0}}{r}}$

Answer 1

Answer: (D)

For a charged soap bubble
$p_{\text {external }}+p_{\text {electro }}=\frac{4 T}{r}$
In equilibrium condition
Surface charge density $\sigma$ is given by
$\sigma^{2}=\frac{8 \varepsilon_{0} T}{r} \Rightarrow \sigma=\sqrt{\frac{8 \varepsilon_{0} T}{r}}$
$\frac{q}{4 \pi r^{2}}=\sqrt{\frac{8 \varepsilon_{0} T}{r}} \Rightarrow \theta=4 \pi \rho^{2} \sqrt{\frac{8 \varepsilon_{0} T}{\rho}}$