If `r` and `T` are radius and surface tension of a spherical soap bubble respectively then find the charge needed to double the radius of bubble.

Explanation

For smalle bubble
`P_(1)=(P_(0)+(4T)/(r))` and `V_(1)=(4)/(3)pir^(3)` for larger bubble
`P_(2)=P_(0)+(4T)/(R)-(sigma^(2))/(2epsilon_(0))` and `V_(2)=(4)/(3)piR^(2)` where `sigma=(q)/(4piR^(2))`
for air inthe bubble `P_(1)V_(1)=P_(2)V_(2) (P_(0)+(4T)/(r))r^(3)=[(P_(0)+(4T)/(R))-(q^(2))/(16pi^(2)R^(4)xx2epsilon_(0))]R^(-3)`
`P_(0)[R^(3)-r^(3)]+4T[R^(2)-r^(2)]P_(0)[R^(3)-r^(3)]+4T[R^(2)-r^(2)]=(q^(2))/(32pi^(2)epsilon_(0)R)=0`
But `R=2r`
`P_(0)[7r^(3)]+4T[3r^(2)]-(q^(2))/(32pi^(2)epsilon_(0)(2r))=0`
`(q^(2))/(64pi^(2)epsilon_(0)r)=7P_(0)r^(3)+12Tr^(2)`
`q^(2)=64pi^(2)epsilon_(0)r^(3)[7P_(0)r+12T]`
`q=8pir[epsilon_(0)r(7P_(0)r+12T)]^(1//2)`