A) \[2\sqrt{\frac{2\,r\,T}{{{\varepsilon }_{0}}}}\]
B) \[8\,\pi \,r\sqrt{2\,r\,T\,{{\varepsilon }_{0}}}\]
C) \[8\,\pi \,r\sqrt{r\,T\,{{\varepsilon }_{0}}}\]
D) \[8\,\pi \,r\sqrt{\frac{2\,r\,T}{{{\varepsilon }_{0}}}}\]
Correct Answer: B
Solution :
Inside pressure must be \[\frac{4T}{r}\] greater than outside pressure in bubble. This excess pressure is provided by charge on bubble. \[\frac{4T}{r}=\frac{{{\sigma }^{2}}}{2{{\varepsilon }_{0}}}\] |
\[\frac{4T}{r}=\frac{{{Q}^{2}}}{16{{\pi }^{2}}{{r}^{4}}\times 2{{\varepsilon }_{0}}}\]\[......\left[ \sigma =\frac{Q}{4\pi {{r}^{2}}} \right]\] |
\[Q=8\pi r\sqrt{2rT{{\varepsilon }_{0}}}\] |
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