A soap bubble of radius 3 cm is charged with surface charge density - such that -2-0 - 0-4 SI units- The excess pressure inside the bubble in SI unit surface tension of soap solution - 3 - 10-3 N-m is-

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Excess Pressure in Bubbles

A soap bubble...

Question

A soap bubble of radius 3 cm is charged with surface charge density $σ$ such that $\frac{σ^{2}}{ϵ_{0}} = 0.4 S I$ units. The excess pressure inside the bubble in SI unit (surface tension of soap solution $= 3 \times 10^{- 3}$ N/m) is:

0.1

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0.2

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0.5

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0.25

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Solution

The correct option is B $0.2$

In a charged soap bubble surface tension T acts inward.
The repulsive force due to charging acts outward.
$\frac{σ^{2}}{2 ϵ_{0}}$ - Pressure due to the repulsive force
$\frac{4 T}{R}$ is the excess pressure due to surface tension
$P_{e x c e s s} = \frac{4 T}{R} - \frac{σ^{2}}{2 ϵ_{0}} = \frac{4 \times 3 \times 10^{- 3}}{3 \times 10^{- 2}} - \frac{0.4}{2} = 0.4 - 0.2 = 0.2$

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A soap bubble of radius 3 cm is charged with surface charge density σ such that σ2ϵ0=0.4 SI units. The excess pressure inside the bubble in SI unit (surface tension of soap solution =3×10−3 N/m) is:

The correct option is B 0.2In a charged soap bubble surface tension T acts inward.The repulsive force due to charging acts outward.σ22ϵ0 - Pressure due to the repulsive force4TR is the excess pressure due to surface tensionPexcess=4TR−σ22ϵ0=4×3×10−33×10−2−0.42=0.4−0.2=0.2

A soap bubble of radius 3 cm is charged with surface charge density $σ$ such that $\frac{σ^{2}}{ϵ_{0}} = 0.4 S I$ units. The excess pressure inside the bubble in SI unit (surface tension of soap solution $= 3 \times 10^{- 3}$ N/m) is: