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AP EAMCET · PHYSICS · Electrostatics

When a soap bubble of radius \(0.2 \mathrm{~mm}\) is charged, it experiences an outward electrostatic pressure of magnitude \(\frac{\sigma^2}{2 \varepsilon_0}\), where \(\sigma=20 \mu \mathrm{Cm}^{-2}\) is the surface charge density. If the excess pressure inside the soap bubble due to the surface tension is same as
this electrostatic pressure, then the surface tension of the soap solution is
\[
\left(\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)
\]

  1. A \(8.85 \times 10^{-4} \mathrm{Nm}^{-1}\)
  2. B \(12.4 \times 10^{-4} \mathrm{Nm}^{-1}\)
  3. C \(11.3 \times 10^{-4} \mathrm{Nm}^{-1}\)
  4. D \(90 \times 10^{-4} \mathrm{Nm}^{-1}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(11.3 \times 10^{-4} \mathrm{Nm}^{-1}\)

Step-by-step Solution

Detailed explanation

Excess pressure inside soap bubble due to surface tension, \(p=\left(\frac{4 S}{R}\right)\), where \(S=\) surface tension and \(R=\) radius. \(\Rightarrow\) Electrostatic pressure, \(p=\frac{\sigma^2}{2 \varepsilon_0}\) According to the question,…
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