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 (${\epsilon }_0=$ permittivity of free space, $T=$ surface tension of soap solution)

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

Answer 1

Answer: (D)

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