In air , a charged soap bubble of radius r is in equilibrium having outside and inside pressures being equal . The charge on the drop is (`epsi_(0)` = permittivity of free space , T = surface tension of soap solution)

Options

A. `4 pi r^(2) sqrt((2 T epsi_(0))/(t))`
B. `4 pi r^(2) sqrt((4 E epsi_(0))/(t))`
C. `4 pi r^(2) sqrt((6 T epsi_(0))/(t))`
D. `4 pi r^(2) sqrt((8 T epsi_(0))/(t))`

Answer

D

Explanation

For a charged soap bubble
`P_("external") + P_("electro") = (4T)/(r)`
In equilibrium condition
Surface charge density `sigma` is given by
`sigma^(2) = (E epsi_(0)T)/(r) implies sigma = sqrt((8 epsi_(0) T)/(r))`
`(q)/(4 pi r^(2)) = sqrt((8 epsi_(0)T)/(r)) implies theta = 4 pi rho^(2) sqrt((8 epsi_(0) T)/(rho))`