A charged soap bubble having surface charge density $σ$ and radius R. If pressure inside soap bubble and pressure outside it is same then the surface tension for soap bubble is

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$T = \frac{σ^{2} R}{8 \in_{0}}$

$T = \frac{σ^{2} R}{4 \in_{0}}$

$T = \frac{σ^{2} R}{2 \in_{0}}$

$T = \frac{σ^{2} R}{\in_{0}}$

answer is A.

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Detailed Solution

$F = (\frac{σ^{2}}{2 \in_{0}}) A$
Since a soap bubble has 2 free surfaces, so $F = 2 T (2 π R)$
$\Rightarrow 2 [T (2 π R)] = \frac{σ^{2}}{2 \in_{0}} (π R^{2})$
$\Rightarrow T = \frac{σ^{2} R}{8 \in_{0}}$

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