Question

Four charge $+q,+q,-q$ and $-q$ are placed respectively at the corners $A,B,C$ and $D$ of a square of side $\left(a\right)$, arranged in the given order. Calculate the intensity of electric field at the center of the square where Q is a charge.

• A. $zero$
• B. $\frac{K4\sqrt{2}qQ}{a^2}$
• C. $\frac{K4qQ}{a^2}$
• D. $\frac{K2\sqrt{2}qQ}{a^2}$

Answer 1

The correct option is B $\frac{K4\sqrt{2}qQ}{a^2}$

Consider the problem

$F_1$ by $-q$ and $+q$ on $Q$ charge

$\begin{array}{c}{F}_1=\frac{kQq}{{\left(\frac{a}{\sqrt{2}}\right)}^2}+\frac{kQq}{{\left(\frac{a}{\sqrt{2}}\right)}^2}\\ =\frac{4kQq}{a^2}N\end{array}$

And

$F_2$ by $-q$ and $+q$ on $Q$ charge

$\begin{array}{c}{F}_2=\frac{kQq}{{\left(\frac{a}{\sqrt{2}}\right)}^2}+\frac{kQq}{{\left(\frac{a}{\sqrt{2}}\right)}^2}\\ =\frac{4kQq}{a^2}N\end{array}$

$F_1=F_2=\frac{4kQq}{a^2}N$

Now $F$ Resultant

$\begin{array}{c}=\sqrt{{\left(F_1\right)}^2+{\left(F_2\right)}^2+2F_1{F}_2\cos {90}^{\circ }}\\ =\sqrt{2}F\\ =\sqrt{2}\left(\frac{4kQq}{a^2}\right)\\ =4\sqrt{2}\frac{kQq}{a^2}\end{array}$

Hence, Option $B$ is the correct answer.