Question

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 :

• A. $\frac{ q }{4 \pi \in_{0} a ^{2}}\left(\frac{1}{\sqrt{2}}+\frac{1}{2}\right)$
• B. $\frac{ q }{4 \pi \in_{0} a ^{2}}\left(1+\frac{1}{\sqrt{2}}\right)$
• C. $\frac{ q }{4 \pi \epsilon_{0} a ^{2}}\left(1-\frac{1}{\sqrt{2}}\right)$
• D. $\frac{ q }{4 \pi \in_{0} a ^{2}}\left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)$

Answer 1

Answer: (A)

$\left( E _{\text {net }}\right)_{ D }=\frac{ kq }{2 a ^{2}}+\frac{\sqrt{2} kq }{2 a ^{2}}$
$\left( E _{\text {net }}\right)_{ D }=\frac{ kq }{ a ^{2}}\left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)$
$\left( E _{\text {net }}\right)_{ D }=\frac{ q }{4 \pi \epsilon_{0} a ^{2}}\left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)$