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In air, a charged soap bubble of radius r is in equilibrium, outside and inside pressures being equal. The charge on the drop is ( ₀= . permittivity of free space, T= surface tension of soap solution),

Options

  1. A4 r² 2 T ₀ r
  2. B4 r² 4 T ₀ r
  3. C4 r² 6 T ₀ r
  4. D4 r² 8 T ₀ r

Correct answer

D. 4 r² 8 T ₀ r

Step-by-step solution

For a charged soap bubble P e x t e r n a l   +   P e l e c t r i c = 4 T r We also know that electrostatic pressure on the patch(small part of the charged surface) E l e c t r o s t a t i c   P r e s s u r e = σ 2 2 ε 0 In equilibrium condition, equating above equations σ 2 2 ε 0 = 4 T r σ 2 = 8 ε 0 T r   ⇒ σ = 8 ε 0 T r   σ = Q A ,   w h e r e   A   i s   s u r f a c e   a r e a   o f   s p h e r i c a l

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