A charged soap bobbe having surface charge density `sigma` and radius r. If the pressure inside and outsides the soap bubble is the same, then the surface tension of the soap solution is

Options

A. `T = (sigma^(2) R )/( 8 epsilon_(0))`
B. `T = (sigma^(2) R )/( 4 epsilon_(0))`
C. `T = (sigma^(2) R )/(2 epsilon_(0))`
D. `T = (sigma^(2) R )/(epsilon_(0))`

Answer

A

Explanation

Excess of Pressure inside liquid bubble
`P_(1) = (4 T)/( R )`
electrostatic pressure due to charge
`P_(2) = (sigma^(2))/(2 epsilon_(0)) `
Comparing them `(4T )/( R ) = (sigma^(2))/(2 epsilon_(0))`
Therefore `T = (sigma^(2) R) /(8 epsilon_(0))`