Solving the Charged Bubble Problem with Gas and Electrostatic Forces

2 replies · 2K views · last reply
Ahmed Farhan
1.
Textbook problem 16: a soap bubble of radius R0 given charge q expands to R, with pressure dropping to p(V0/V); asks to show q^2 = 32π^2 ε0 p R(R^3 − R0^3), with a hint on forces.
2. The force due to gas pressure = p(V0/V) dA
The force due to atmospheric pressure = p dA
The force due to electrostatic repulsion = undetermined

3. Though I don't surely know what the expression for electric force should be, I took an educated guess and solved using the relation:
force of gas pressure + electric repulsion = atmospheric pressure force
but couldn't get the expression asked for in the problem. Can anyone please take a look?
 

Discussion

Please show details of your attempt. The question refers to problem 15. Is there anything in that problem that you could list as relevant to this problem?
 
electrostatic pressure = σ2/2ε0
where σ=q/(4πR2)
now,
pV0/V + σ2/2ε = p
V0=4/3*π*R03 and V=4/3*π*R3
this follows the result