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 $\eta$. The system of charges and planar film are in equilibrium, and $a=k{\left[\frac{q^2}{\gamma }\right]}^{1/N}$, where k is a constant. Find the value of N. ___

Answer 1

$F_{electric}=\frac{k{q}^2}{2a^2}+2[\frac{k{q}^2}{a^2}\times \frac{1}{\sqrt{2}}]=\frac{q^2}{a^2}\times constant$
As the system of charges and planar film is in equilibrium, $\frac{q^2}{a^2}\times constant=\gamma a.constant$
$\therefore a=k{\left[\frac{q^2}{\gamma }\right]}^{1/3}$
$\therefore N=3$