Question

An isolated and charged spherical soap bubble has radius 'r' and the pressure inside is atmosphere if 'T' is the surface tension of soap solution, then charge on drop is

• A. $\sqrt{\frac{2rT}{{\epsilon }_o}}$
• B. $8\pi r\sqrt{2rT{\epsilon }_o}$
• C. $8\pi r\sqrt{rT{\epsilon }_o}$
• D. $8\pi r\sqrt{\frac{2rT}{{\epsilon }_o}}$

Answer 1

Answer: (B)

$8\pi r\sqrt{2rT{\epsilon }_o}$

$\text{We know that}$

$T=\frac{\epsilon }{A}$

$\epsilon =2AT=\pi r^{2}T$

$\text{a}nd$

$\epsilon =\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r}$

$\Rightarrow 2\pi r^{2}T=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r}$

$q=8\pi r\sqrt{2rT{\epsilon }_0}$

$\text{Answer:-(B)}$