Physics - Elecrostatics Question with Solution | TestHub

$F_1=$ Net electrostatic force on anyone charge due to rest of three charges $$=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{a^2}\left(\sqrt{2}+\frac{1}{2}\right)$$ $F_2=$ Surface tension force $=\gamma a$ If we see the equilibrium of line $BC$, then, $2F_1\cos 45^{\circ }=F_2$ or $\sqrt{2}{F}_1=F_2$ or $\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{a^2}\left(2+\frac{1}{\sqrt{2}}\right)=\gamma a$ $\therefore a^3=\frac{1}{4\pi {\epsilon }_0}\left(2+\frac{1}{\sqrt{2}}\right)\frac{q^2}{\gamma }$ or $a={\left\{\frac{1}{4\pi {\epsilon }_0}\left(2+\frac{1}{\sqrt{2}}\right)\right\}}^{1/3}{\left[\frac{q^2}{\gamma }\right]}^{1/3}$ $=k{\left[\frac{q^2}{\gamma }\right]}^{1/3}$ where, $k={\left\{\frac{1}{4\pi {\epsilon }_0}\left(2+\frac{1}{\sqrt{2}}\right)\right\}}^{1/3}$ Therefore, $N=3$ Answer is 3 . Analysis of Question (i) Question is moderately difficult. (ii) In my opinion problems of surface tension or viscosity are always not very simple questions.