A charged soap bubble of radius $R$ and surface tension $T$ is in equilibrium with outside and insid

Question

A charged soap bubble of radius $R$ and surface tension $T$ is in equilibrium with outside and inside pressures equal. The charge on the soap bubble is equal to\

Professor PC Thomas Classes · Answer

For equilibrium, Electrostatic pressure = excess pressure\ $\frac{\sigma^{2}}{2 \varepsilon_{0}}=\frac{4 \mathrm{~T}}{\mathrm{R}}$\ $\sigma^{2}=\frac{8 \varepsilon_{0} T}{R} \quad \sigma=\sqrt{\frac{8 \varepsilon_{0} T}{R}}$\ charge $Q=4 \pi R^{2} \quad \sigma=4 \pi R^{2} \sqrt{\frac{8 \varepsilon_{0} T}{R}}$\ $=\sqrt{16 \pi^{2} R^{4} 	imes \frac{8 \varepsilon_{0} T}{R}}=\sqrt{128 \pi^{2} R^{3} \varepsilon_{0} T}$\