The radius of a soap bubble is r and the surface tension of the soap solution is S. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is
$(ϵ_{0} =)$ permittivity of the free space

Question

The radius of a soap bubble is r and the surface tension of the soap solution is S. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is

(ϵ_{0} =)

permittivity of the free space

Accepted Answer

Correct answer: D. (d) Since pressure difference due to surface tension, p_i-p_0= 4Sr Electrostatic pressure due to change on the soap bubble, = ^22 _0 Here, = surface charge density and _0= permitivity of the free space Electric potential on spherical shell, V= kqr ⇒V= k ( σA )r [ asq= A ] Putting, A=4 r^2 and k= 14 _0 V= 14 _0 ( 4 r^2r )= σr _0 ⇒ = _0Vr Pressure difference due to, surface tension must .cancel pressure difference due to charge. ⇒ 4Sr= ^22 _0 ⇒ 4Sr= ( _0Vr )^22 _0 ⇒V= 8 Sr _0 So, the potential of the bubble is 8 Sr _0.

$The radius of a soap bubble is r and the surface tension of the soap solution is S. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is (ϵ_{0} =) permittivity of the free space$

Solution

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