$(a)\;144\times10^{4}\;\large\frac{(5 \sqrt{5}+1)}{\sqrt{5}}\qquad(b)\;72\times10^{4}\;\large\frac{(5 \sqrt{5}+1)}{\sqrt{5}}\qquad(c)\;36\times10^{4}\;\large\frac{(5 \sqrt{5}+1)}{\sqrt{5}}\qquad(d)\;None$

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Answer : (a) $\;144\times10^{4}\;\large\frac{(5 \sqrt{5}+1)}{\sqrt{5}}$

Explanation :

E= $\large\frac{9\times10^{9}\times10^{-6}}{(\large\frac{0.1}{2})^2}$

$|E|=9\times4\times10^{3}\times10^2$

$|E|=36\times10^{5}$

$|E_{1}|=\large\frac{9\times10^{9}\times10^{-6}}{(\sqrt{5}\times\large\frac{0.1}{2})^2}$

$=\large\frac{36}{5}\times10^5$

$|E_{net}|=2|E| +2|E_{1}|+2|E_{1}|cos \theta\quad ; cos \theta=\large\frac{1}{\sqrt{5}}$

$=2 (36\times10^{5} + \large\frac{36}{5}\times10^{5} \times \large\frac{1}{\sqrt{5}})$

$=\large\frac{72\times10^5\;(5 \sqrt{5}+1)}{5 \sqrt{5}}$

$=144\times10^{4}\;\large\frac{(5 \sqrt{5}+1)}{\sqrt{5}}\;.$

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