Electrostatics Question 656
Question: A soap bubble (surface tension =$ T $ ) is charged to a maximum surface density of charge =$ \sigma $ . When it is just going to burst? Its radius R is given by
Options:
A) $ R=\frac{{{\sigma }^{2}}}{8{\varepsilon _{0}}T} $
B) $ R=8{\varepsilon _{0}}\frac{T}{{{\sigma }^{2}}} $
C) $ R=\frac{{{\sigma }^{{}}}}{\sqrt{8{\varepsilon _{0}}T}} $
D) $ R=\frac{{{\sqrt{8{\varepsilon _{0}}T}}^{{}}}}{\sigma } $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] The pressure due to surface tension $ =\frac{4T}{R} $ The pressure due to electrostatic forces $ =\frac{{{\sigma }^{2}}}{2{\varepsilon _{0}}} $ Just before the bubble bursts. $ \frac{4T}{R}=\frac{{{\sigma }^{2}}}{2{\varepsilon _{0}}} $ or $ R=\frac{8T{\varepsilon _{0}}}{{{\sigma }^{2}}} $
