Charging a soap bubble

When you provide some charge to a soap bubble, due to the repelling force between the charges, they will try to be as far as possible to minimize the overall potential energy. Also, this is facilitated by the hydrophilic end of the soap molecules. Hydrophilic ends are usually in contact with the air, on the outside and inside surfaces of the soap bubble and the ionic nature of these will help in uniform spreading of the charges.

Now, we have a soap bubble whose surface is uniformly charged, this uniform distribution minimizes the potential energy and no other distribution without changing the size of the bubble has lower energy.

The bubble can increase in size and since increase in the surface area of the bubble further reduces the charge density, this will further reduce the electrostatic potential. But, the issue is by increasing in size, there will be a pressure difference between the inside and the outside of the bubble. This pressure difference will try to squeeze the bubble smaller.

Another situation can be, when the pressure difference across the wall of the bubble is able to cause diffusion of air across the bubble. Then it will result in increase in the size of the bubble and cause an increase in the concentration of smaller molecules, like hydrogen, inside the bubble as compared to the outside. This is due to the preferential diffusion of smaller molecules.

It will expand and there will be an concentration increase of smaller molecules inside, due to diffusion.

But, if there is diffusion, the pressure difference will be reduced and this will cause further expansion. Finally a state will be reached, when the pressure difference, due to charge repulsion, across the bubble wall is lower than that is required for diffusion.

That will be the end of the bubble-world-expansion. Sob! Sob!...

For an unelectrified soap bubble force due to excess pressure from inside is balanced by the force due to surface tension. when it is given an electric charge, there is an outward normal force( $\frac{\sigma^{2}}{2\epsilon_{0}}$ per unit area) that expands the bubble.

The soap bubble is neutralized before we charge it. When the soap bubble is charge, the negative charges are not equals therefore is generated a electric force and the charges must move to a distance to reach the electric equilibrium