Finding Charge to Double Bubble Radius: Homework Solution

[Kishor Bhat]

Homework Statement

Find the amount of charge required to double the radius of a bubble of radius r and surface tension T.

Homework Equations

Increase in surface energy of bubble = T ΔA

The Attempt at a Solution

I've tried equating the increase in surface energy to the work done by the Coulomb force, but I'm finding a lack of information. Do I just assume that the charge is some distance away from the bubble? Then what will be the integration limits for F . dr?

 

[anathema]

I would like to clarify a few things before attempting to solve this problem. Firstly, what is the context of this bubble? Is it a soap bubble or a gas bubble in a liquid? This will affect the surface tension value used in the calculation. Additionally, is the bubble in a vacuum or a specific medium? This will also affect the calculation.

Assuming that the bubble is a soap bubble in air, the following approach can be taken:

1. Determine the increase in surface energy of the bubble when its radius is doubled. This can be calculated using the equation given in the homework statement:
Increase in surface energy = T ΔA = T (4πr^2)

2. Convert the increase in surface energy to work done by the Coulomb force. This can be done by equating the work done by the Coulomb force to the increase in surface energy:
W = Fd = T (4πr^2)

3. Determine the distance d between the bubble and the charge. This will depend on the specific setup of the bubble and the charge. If the charge is a point charge, then the distance will be the radius of the bubble (r). If the charge is distributed over a surface, then the distance will be the distance between the center of the bubble and the center of the charge distribution.

4. Finally, use the equation for Coulomb's law to solve for the amount of charge required:
F = k(Qq)/d^2
Where:
k = Coulomb's constant
Q = charge of the bubble (unknown)
q = charge of the external charge (unknown)
d = distance between the bubble and the external charge

By substituting the values obtained in steps 1-3, the equation can be solved for Q, giving the amount of charge required to double the radius of the bubble.

It is important to note that this approach assumes a simplified scenario and may not accurately reflect the real-world situation. Additional information and data may be needed to make a more accurate calculation.