Four charges $+q$,$+q$,$-q$, and $-q$ are placed on $X-Y$ plane at the points whose coordinates are $\left(0.5, 0\right)$, $\left(0, 0.5\right)$, $\left(-0.5, 0\right)$ and $\left(0, -0.5\right)$ respectively.



The electric field due to these charges at a point $P\left(r,r\right)$, where $r>>0.5$, will be

The four charges can be considered two dipoles of equal magnitude and directed along the +x axis and +y axis.
The magnitude of dipole moment = q x (distance between positive and negative charges on x-axis)

$p=q\times 1=q$

The resultant dipole moment of these two dipoles with be, $p_{\text{r}}=\sqrt{q^2+q^2}=q\sqrt{2}$
The direction of the resultant dipole moment will be at $45°$ from the x-axis
The distance of the point $(r, r)$ from the dipole is $r\sqrt{2}m$
The resultant electric field is

    $E=\frac{1}{4\pi {\epsilon }_0}\times \frac{2p_r}{{\left(r\sqrt{2}\right)}^3}$

      $=\frac{1}{4\pi {\epsilon }_0}\times \frac{2\times q\sqrt{2}}{2\sqrt{2}{r}^3}$

      $=\frac{1}{4\pi {\epsilon }_0}\times \frac{q}{r^3}$