The radius of a spherical soap bubble is r and surface tension of soap water is T respectively. Find the charge uniformly distributed over the outer surface of the bubble is required to double its radius. (Atmospheric pressure is Po and inside temperature of the bubble during expansion remain constant)
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a
8πrϵ0r7P0r+16T1/2
b
4πr∈0r7P0r+8T1/2
c
πr∈0r7P0r+12T1/2
d
8πrϵ0r4P0r+12T1/2
answer is A.
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Detailed Solution
Before charging the bubble pressure inside the bubble P1=P0+4TrAfter charging electrostatic pressure will be σ22ϵ0When radius becomes 2r then P18+σ22ϵ0=Po+4T2rWhere σ=q4π(2r)2