A small electric dipole is placed at origin with its dipole moment directed along positive x-axis. The direction of electric field at point $(2,2\sqrt{2},0)$ is

Given data: Electric dipole and the direction of electric field

Concept used: Electric dipole and fields

Detailed solution:

$$\begin{gathered} \tan \theta =\frac{y}{x}=\frac{2\sqrt{2}}{2}=\sqrt{2} \\ \Rightarrow \cot \theta =\frac{1}{\sqrt{2}} \end{gathered}$$

$$\begin{gathered} \tan \varphi =\frac{E_{\theta }}{E_r}=\frac{\tan \theta }{2} \\ =\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}} \end{gathered}$$

$$\begin{gathered} \tan \varphi =\cot \theta \\ \tan \varphi =\tan \left(90-\theta \right) \\ \Rightarrow \varphi +\theta =90 \end{gathered}$$

i.e., E is along positive Y-axis