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 $a=k{\left[\frac{q^2}{\gamma }\right]}^{1/N},$ where 'k' is a constant,. Then N is

Answer 1

$(2\times a\times \gamma )\times c=2\times \{\frac{k{q}^2}{a^2}+\frac{k{q}^2}{2a^2}\times \frac{1}{\sqrt{2}}\}$

$\Rightarrow a^3=k\left\{\frac{q^2}{\gamma }\right\}\{1+\frac{1}{2\sqrt{2}}\}$

$\Rightarrow a^3=k^{\prime }\left\{\frac{q^2}{\gamma }\right\}$

$\Rightarrow a=k^{\prime \prime }{\left\{\frac{q^2}{\gamma }\right\}}^{\frac{1}{3}}$