Question

Four point charges, each of $+q$, are rigidly fixed at the four corners of a square planar soap film of side ` $a$ `. The surface tension of the soap film is $\gamma$ The system of charges and planar film are in equilibrium, and $a=k[\frac{q^2}{\gamma }{]}^{1/N}$, where '$k$' is a constant. Then $N$ is:

• A. 3
• B. 2
• C. 4
• D. 9

Answer 1

The correct option is A 3

Net electrostatic force on one charge
$=\frac{1}{4\pi {ϵ}_o}\frac{q^2}{a^2}[\frac{1}{2}+\sqrt{2}]$
Considering MN as system,
$\frac{1}{4\pi {ϵ}_o}\frac{q^2}{a^2}[\frac{1}{2}+\sqrt{2}]\times 2cos{45}^o=2\gamma a$
or
$a=k{\left[\frac{q^2}{r}\right]}^{1/3}$
Thus $N=3$