Question

A charged soap bubble having surface charge density $\sigma $ and radius $r$ . If the pressure inside and outside the soap bubble is the same, then the surface tension of the soap solution is

• A. $T=\frac{\sigma ^{2} R}{8 \epsilon _{0}}$
• B. $T=\frac{\sigma ^{2} R}{4 \epsilon _{0}}$
• C. $T=\frac{\sigma ^{2} R}{2 \epsilon _{0}}$
• D. $T=\frac{\sigma ^{2} R}{\epsilon _{0}}$

Answer 1

Answer: (A)

Excess of Pressure inside liquid bubble $P_{1}=\frac{4 T}{R}$
electrostatic pressure due to charge $P_{2}=\frac{\sigma ^{2}}{2 \epsilon _{0}}$
Comparing them $\frac{4 T}{R}=\frac{\sigma ^{2}}{2 \epsilon _{0}}$
Therefore $T=\frac{\sigma ^{2} R}{8 \epsilon _{0}}$