If the bubble is surrounded by dry air. there is a maximum value the charge q ca

Question

If the bubble is surrounded by dry air. there is a maximum value the charge q can have, hence a maximum delta r. Calculate the maximum value of delta r for r0 = 5.00 cm and P0 = 101.3 kPa. Would it be practical to measure the expansion under these circumstances? A spherical soap bubble of radius r0 is given an electric charge q. The resulting electrostatic stress causes the bubble to expand slightly, to radius r0 + delta r. Calculate delta r, in terms of the original radius r0, the charge q, and the original pressure P0 within the bubble. HINTS: The size of the uncharged soap bubble is set by the equilibrium between the air pressure difference inside and outside the bubble (the pressure inside is slightly higher) and the surface tension of the soap film (which tends to contract the bubble). The expansion of the charged bubble lowers the interior pressure, but the outward electrostatic stress makes up the difference. Assume that the surface tension remains unchanged. Assume also that the amount and temperature of the gas inside the bubble do not change; recall that the air in the bubble obeys the Ideal Gas Law: PV = nRT , with pressure P, volume V, number of moles n, gas constant R, and absolute temperature T. Make use of the fact that the changes in bubble radius, pressure, etc., are small.

Explanation / Answer

(Delta r=(q^{2}epsilon_{0})/(96pi^{2}r_{0}^{3}P_{0}))

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