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An isolated soap bubble is kept in a container in which the pressure is maintained at P 0 . The bubble is given some charge due to which its radius increases to r and the pressure inside the bubble reduces to P 0 . If the surface tension of the soap bubble is T , then the charge given to the bubble is

Options

  1. AQ = 8 π r r T ε 0
  2. BQ = 8 π r 2 r T ε 0
  3. CQ = 4 π r 2 r T ε 0
  4. DQ = 4 π r r T ε 0

Correct answer

B. Q = 8 π r 2 r T ε 0

Step-by-step solution

The excess pressure inside a soap bubble due to surface tension is 4 T r . In the given problem the pressure of the air inside and outside the bubble is the same, hence the excess pressure in this situation should be due to the electrostatic pressure. 4 T r = σ 2 2 ε 0 ⇒ 4 T r = 1 2 ε 0 Q 4 π r 2 2 ⇒ Q = 8 π r 2 r T ε 0

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