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Q.

A soap bubble (surface tension = T) is charged to a maximum surface density of charge = $σ$ . When it is just going to burst, its radius R is given by

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a

$R = \frac{σ^{2}}{8 ε_{0} T}$

b

$R = 8 ε_{0} \frac{T}{σ^{2}}$

c

$R = \frac{σ}{\sqrt{8 ε_{0} T}}$

d

$R = \frac{\sqrt{8 ε_{0} T}}{σ}$

answer is B.

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Detailed Solution

The pressure due to surface tension $= \frac{4 T}{R}$

The pressure due to electrostatic forces $= \frac{σ^{2}}{2 ε_{0}}$

Just before the bubble bursts.

$\frac{4 T}{R} = \frac{σ^{2}}{2 ε_{0}} or R = \frac{8 T ε_{0}}{σ^{2}}$

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A soap bubble (surface tension = T) is charged to a maximum surface density of charge = σ. When it is just going to burst, its radius R is given by