Question

A soap bubble is given negative charge, its radius will :

• A. increase
• B. decrease
• C. remain unchanged
• D. fluctuate

Answer 1

The correct option is A increase

For a soap bubble (electrified)
Excess pressure$=P=P_i-P_o=\frac{4T}{r}$
$T=$ surface tension, $r=$radius
Force due to excess pressure balances surface tension
When bubble is charged
$P_{excess}=P_{electrostatic}+\frac{4T}{r}$
$P_{electrostatic}=-\frac{{\sigma }^2}{2{\epsilon }_0}=-\frac{1}{2{\epsilon }_0}\frac{q^2}{16{\pi }^2{r}^4}$
$P_{excess}=\frac{4}{r}[T-\frac{q^2}{128{\pi }^2{\epsilon }_0{r}^3}]....\left(A\right)$
Surface tension decreases. $(P\propto \frac{1}{r})$, means radius increases. In equation $\left(A\right)$, $q^2$ is not affected by positive or negative charge hence , whether it is given a positive or negative charge it always expands in radius.