An isolated charged soap bubble of radius R0 = 6.65 cm is at a potential of V0 =

Question

An isolated charged soap bubble of radius R0 = 6.65 cm is at a potential of V0 = 223.0 volts. If the bubble shrinks to a radius that is 27.0% of the initial radius, by how much does its electrostatic potential energy U change? Assume that the charge on the bubble is spread evenly over the surface, and that the total charge on the bubble remains constant.

An isolated charged soap bubble of radius Ro-6.65 cm is at a potential of Vo 223.0 volts. If the bubble shrinks to a radius that is 27.0% of the initial radius, by how much does its electrostatic potential energy U change? Assume that the charge on the bubble is spread evenly over the surface, and that the total charge on the bubble remains constant. Number U= Ufinal-U.nitial = 10

Explanation / Answer

Energy stored in uniformly distributed charged sphere
U = V2R/2k
where V is the potential of sphere and equal to kq/R
V= kq/R   .........1
R is radius of sphere
k is constant.
V1 = kq/R1
V2 = kq/R2 = kq/0.27R1
V2/V1 = 1/0.27
V2 = V1/0.27

Uinitial = V12 R1 / 2k
Ufinal = V22 R2 / 2k = V12 R1 / 2k*0.27
Ufinal - Uinitial = (V12 R1 / 2k) (1/0.27 -1)
                       = (2232 * 0.0665/2*9x109) ( 1/0.27 -1)
                          = 4.97x10-7 J

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