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A charged, isolated spherical soap bubble of radius r has internal pressure equal to atmospheric pressure. If the charge on the bubble is given by Xπ√(2Tε), what is the value of X?

1. 8
2. 9
3. 7
4. 2

Correct answer: 8

Solution

Internal = atmospheric means surface-tension excess pressure 4T/r equals outward electrostatic pressure sigma^2/(2*eps0), with sigma = Q/(4*pi*r^2). Solving gives Q = 8*pi*sqrt(2*T*eps0)*r^(3/2), so X = 8.

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