Question

Four point charges each of charge $+q$ are rigidly fixed at the four corners of a square planar soap film of side $a$. The surface tension of the soap film is $S$. The system of charges and planar film are in equilibrium, and $a=k(\frac{q}{S}{)}^{1/N}$ where $k$ is a constant. Find the value of $N$.

Answer 1

Surface tension = $S$

Force on $+q$ due to other three charges is

$E_A=E_C=\frac{Kq}{a^2}{E}_B=\frac{Kq}{{2a}^2}{E}_{net}=E_B+\sqrt{{E_A}^2+{E_C}^2}=\frac{Kq}{{2a}^2}+\sqrt{2}\frac{Kq}{a^2}⟹\frac{q}{a^2}(\frac{K}{2}+K\sqrt{2})$

Force due to surface tension = $S.a=\frac{q}{a^2}K$

$⟹\frac{q^{1/3}}{S}{K}^{1/3}$

$\therefore N=3$