# Charged Bubble Oscillation

kenth
Homework Statement:
A bubble with radius ##R##, mass ##m## and surface tension ##S## has initial pressure inside ##P_i## and outside pressure ##P_0## then charged with surface charge density ##\sigma##, Find the period of the oscillation
Relevant Equations:
Gauss's Law, Laplace equation, Newton's Law of Motion
From Gauss's Law

give ##E=\dfrac{\sigma}{2\epsilon_0}##

##\therefore P_e=\dfrac{\sigma^2}{2\epsilon_0}##

Consider at equilibrium (before bubble being charged)

##P_i=P_0+\dfrac{4S}{R}##

Using Newton's 2nd Law

##\Sigma F=m\ddot{R}##

Let ##R+\delta R## be the new radius

Give (after binomial approximation) ##\dfrac{\sigma^2}{2\epsilon_0}+\dfrac{4S\delta R}{R^2}=\dfrac{m}{\pi R^2}\ddot{R}##

I think this should be SHM but the equation doesn't look like it, also do I need to consider the fact that ##P_i## decreases due to change in volume?

Last edited:
Delta2