In air,a charged soap bubble of radius R brea | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the charge on the big bubble be $Q$ and its radius be $R$. The charge density is $\sigma = \frac{Q}{4\pi R^2}$.The mechanical force per unit a

Vedclass · Accepted Answer

$16: 1$

Vedclass · Answer

(A) Let the charge on the big bubble be $Q$ and its radius be $R$. The charge density is $\sigma = \frac{Q}{4\pi R^2}$.The mechanical force per unit area (electrostatic pressure) on a charged bubble is given by $P = \frac{\sigma^2}{2\epsilon_0} = \frac{Q^2}{2\epsilon_0 (4\pi R^2)^2} = \frac{Q^2}{32\pi^2 \epsilon_0 R^4}$.When the bubble breaks into $64$ small bubbles,the volume is conserved: $\frac{4}{3}\pi R^3 = 64 	imes \frac{4}{3}\pi r^3$,which gives $R^3 = 64r^3$,so $R = 4r$.The total charge $Q$ is conserved,so each small bubble has charge $q = \frac{Q}{64}$.The electrostatic pressure on a small bubble is $p = \frac{q^2}{32\pi^2 \epsilon_0 r^4} = \frac{(Q/64)^2}{32\pi^2 \epsilon_0 (R/4)^4} = \frac{Q^2 / 64^2}{32\pi^2 \epsilon_0 (R^4 / 256)} = \frac{Q^2}{32\pi^2 \epsilon_0 R^4} 	imes \frac{256}{4096} = P 	imes \frac{1}{16}$.Therefore,the ratio of the mechanical force per unit area of the big bubble to that of a small bubble is $P/p = 16:1$.

In air,a charged soap bubble of radius $R$ breaks into $64$ small soap bubbles of equal radius $r$. The ratio of mechanical force per unit area of the big soap bubble to that of a small bubble is

Similar Questions

The excess pressure inside a spherical soap bubble of radius $1 \,cm$ is balanced by a column of oil (specific gravity $= 0.8$), $2 \,mm$ high. The surface tension of the bubble is: (in $\,N/m$)

If a cube of ice is placed in gravity-free space,what happens when the ice melts?

Two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

Two spherical soap bubbles of radii $r_{1}$ and $r_{2}$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to -

If the shape of the liquid surface is curved, then

Vedclass Test Series

Exam Paper Generator

Online Exam Module