• # question_answer The minimum value of $|{{z}_{1}}-{{z}_{2}}|$ and ${{z}_{1}}$and${{z}_{2}}$ vary over the curve $|\sqrt{3}\,(1-2z)\,+2i\,|\,=2\sqrt{7}$ and $|\sqrt{3}\,(-1-z)\,-2i\,|\,=\,|\,\,\sqrt{3}\,(9-z)+18i\,\,|,$ respectively. A)  $\frac{7\sqrt{7}}{2\sqrt{3}}$                      B)  $\frac{5\sqrt{7}}{\sqrt{3}}$ C)  $\frac{14\sqrt{7}}{\sqrt{3}}$                      D)  $\frac{7\sqrt{7}}{5\sqrt{3}}$

$\therefore$ $F=\frac{1}{r\pi {{\varepsilon }_{0}}}\frac{Q(Q-q)}{{{R}^{2}}}$      $\frac{dF}{dq}=0$ Represents a perpendicular bisector of the line segment joining $\frac{d}{dq}\,\left[ \frac{Kq(Q-q)}{{{R}^{2}}} \right]=0$  and $\Rightarrow$ is $[Q-2q]=0$ Equation of perpendicular bisector of AB is $q=\frac{Q}{2}$ $U=\frac{{{Q}^{2}}}{2C}$         $C'=KC$ $U'=\frac{{{Q}^{2}}}{2C'}=\frac{1}{2}\,\frac{{{Q}^{2}}}{KC}$   $\therefore$ $\frac{U}{U'}=\frac{{{Q}^{2}}/2C}{{{Q}^{2}}/2KC}=K$   ${{R}_{\min }}=\frac{r}{n}$ ${{R}_{\max }}=nr$ Minimum value of $\therefore$ = Perpendicular distance of centre of circle to the line - Radius of circle $\frac{{{R}_{\min }}}{{{R}_{\max }}}=\frac{r}{n}\times \frac{1}{nr}=\frac{1}{{{n}^{2}}}$ $=0.1\times 0.05=5\times {{10}^{-3}}\,{{m}^{2}},$ $\Delta \phi =-0.05\times {{10}^{-3}}$