A conducting liquid bubble of radius a and thickness ` t ( tltlt a)` is charged to potential `V`. If the bubble collapses to a droplet , find the potential on the droplet .

Options

A. `V((a)/(3t))^(1//2)`
B. `V((2a)/(3t))^(1//3)`
C. `V((a)/(3t))^(1//3)`
D. `V`

Answer

A

Explanation

`V=(1)/(4piepsilon_(0))(q)/(a) q=4piepsilon_(0)aV`
Equation volumes of bubble and droplet
`4pia^(2)t=(4)/(3)piR^(3) R=(3a^(2)t)^(1//3)`
`V^(x)=(1)/(4piepsilon_(0))(q)/(R)=(1)/(4piepsilon_(0))(4piepsilon_(0)aV)/((3a^(2)t)^(1//3))=V((a)/(3t))^(1/3)`