A charged soap bubble having surface charge density σ and radius r . If the pressure inside and outside the soap bubble is the same, then the surface tension of the soap solution is

Question

A charged soap bubble having surface charge density σ and radius r . If the pressure inside and outside the soap bubble is the same, then the surface tension of the soap solution is (A) T=(σ 2 R/8 ϵ 0) (B) T=(σ 2 R/4 ϵ 0) (C) T=(σ 2 R/2 ϵ 0) (D) T=(σ 2 R/ϵ 0)

Tardigrade Admin · Accepted Answer

Excess of Pressure inside liquid bubble P1=(4 T/R) electrostatic pressure due to charge P2=(σ 2/2 ϵ 0) Comparing them (4 T/R)=(σ 2/2 ϵ 0) Therefore T=(σ 2 R/8 ϵ 0)

Q. A charged soap bubble having surface charge density $σ$ and radius $r$ . If the pressure inside and outside the soap bubble is the same, then the surface tension of the soap solution is

$T = \frac{σ ^{2} R}{8 ϵ _{0}}$

$T = \frac{σ ^{2} R}{4 ϵ _{0}}$

$T = \frac{σ ^{2} R}{2 ϵ _{0}}$

$T = \frac{σ ^{2} R}{ϵ _{0}}$

Excess of Pressure inside liquid bubble $P_{1} = \frac{4 T}{R}$
electrostatic pressure due to charge $P_{2} = \frac{σ ^{2}}{2 ϵ _{0}}$
Comparing them $\frac{4 T}{R} = \frac{σ ^{2}}{2 ϵ _{0}}$
Therefore $T = \frac{σ ^{2} R}{8 ϵ _{0}}$

Q. A charged soap bubble having surface charge density σ and radius r . If the pressure inside and outside the soap bubble is the same, then the surface tension of the soap solution is

T=8ϵ0​σ2R​

T=4ϵ0​σ2R​

T=2ϵ0​σ2R​

T=ϵ0​σ2R​