The magnitude of electric field intensity at point $\left(2,0,0\right)m$ due to a short dipole of dipole moment, $\overrightarrow{P}=\hat{i}+\sqrt{3}\hat{j}$ coulomb metre kept with its centre at origin is _____ $N{C}^{-1}\left(Take\frac{1}{4\pi {\epsilon }_0}=K\right)$

$$\begin{gathered} \tan \theta =\frac{P_y}{P_x}=\frac{\sqrt{3}}{1} \\ \theta =60° \\ P=\sqrt{{\left(1\right)}^2+{\left(\sqrt{3}\right)}^2}=2 \\ r=2 \end{gathered}$$

The dipole moment makes an angle ${60}^0$ with $X-$ axis and lies in $X-Y$  plane as shown in figure. The electric field at point A due to dipole is

$E=\frac{kP}{r^3}\sqrt{1+3{\cos }^2\theta }$ where $\theta ={60}^0$

$\therefore E=\frac{\sqrt{7}K}{8}$