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. $\frac{q}{4\pi {ϵ}_0{a}^2}\left(1-\frac{1}{\sqrt{2}}\right)$
• D. $\frac{q}{4\pi {\in }_0{a}^2}\left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)$

Answer 1

Answer: (A)

${\left(E_{\text{net }}\right)}_D=\frac{kq}{2a^2}+\frac{\sqrt{2}kq}{2a^2}$
${\left(E_{\text{net }}\right)}_D=\frac{kq}{a^2}\left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)$
${\left(E_{\text{net }}\right)}_D=\frac{q}{4\pi {ϵ}_0{a}^2}\left(\frac{1}{2}+\frac{1}{\sqrt{2}}\right)$