A soap bubble of radius r and surface tension 'T' is given a potential of `V` volt. Show that the new radius 'R' of the bubble is related to its intial radius by eqation,
`p_(0)[R^(3)-r^(3)]+4T[R^(2)-r^(2)]0-epsilon_(0)V^(2)R//2=0`
where , `p_(0)` is the atmosphere pressure.

Answer

A

Explanation

`p_(1)V_(1)=p_(2)V_(2)`
`:. (p_(0)+(4T)/(R )) ((4)/(3) pi R^(3))=(p_(0)+(4T)/(2R)-(sigma^(2))/(2 epsilon_(0))) ((4)/(3) pi)(2R)^(3)`
Here, `sigma=(q)/(A)=(q)/(4 pi (2R)^(2))`.