A conducting bubble of radius a, thickness t ( lt lt a) has a potential V. Now the bubble transforms into a droplet. Find the potential on the surface of the droplet.

Explanation

Let q be the charge on the bubble
The potential on the surface of the bubble , `V = 1/(4 pi epsilon_(0))q/a`
`:. Q = (Va)/k` [ where `k = 1/(4 pi epsilon_(0))]` ……….(1)
Let R be the radius of the droplet.
By comparing their volumes, we get
`(4 pi a^(2))t = 4/3 pi R^(3)`
`:. R = (3a^(2)t)^(1//3)`
Now potential on the surface of the droplet becomes
`V_(1) = (kq)/R`
or, `V_(1) = k((Va)/(k))/((3a^(2)t)^(1//3))` [ from equation (1)]
`:. V_(1) = V((a)/(3t))^(1//3)`.