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The three charges $q / 2, q$ and $q / 2$ are placed at the corners $A , B$ and $C$ of a square of side ' $a$ ' as shown in figure. The magnitude of electric field $(E)$ at the comer $D$ of the square, is
$\frac{ q }{4 \pi \epsilon_{0} a ^{2}}\left(\frac{1}{\sqrt{2}}+\frac{1}{2}\right)$
$\frac{ q }{4 \pi \in_{0} a ^{2}}\left(1+\frac{1}{\sqrt{2}}\right)$
$\frac{ q }{4 \pi \epsilon_{0} a ^{2}}\left(1-\frac{1}{\sqrt{2}}\right)$
$\frac{ q }{4 \pi \in_{0} a ^{2}}\left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)$
Solution
$\left( E _{\text {ner }}\right)_{D}=\frac{ kq }{2 a ^{2}}+\frac{\sqrt{2 kq }}{2 a ^{2}}$
$\left( E _{\text {ner }}\right)_{ D }=\frac{ kq }{ a ^{2}}\left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)$
$\left( E _{\text {net }}\right)_{ D }=\frac{ q }{4 \pi \epsilon_{0} a ^{2}}\left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)$
