List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude $$p$$, oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance $$2r$$ apart along the $$x$$ direction. The midpoint of the line joining the two dipoles is $$X$$. The possible resultant electric fields $$\vec{E}$$ at $$X$$ are given in List-II.

Choose the option that describes the correct match between the entries in List-I to those in List-II.

$$\text{Distance from each dipole to midpoint } X = r$$

$$\vec{E}_{\text{axial}} = \frac{2p}{4\pi\varepsilon_0 r^3}\hat{u}_{\text{axial}}, \quad \vec{E}_{\text{equatorial}} = -\frac{p}{4\pi\varepsilon_0 r^3}\hat{u}_{\text{equatorial}}$$

Evaluating entry (P):

$$\vec{p}_1 = p\hat{j} \quad (\text{equatorial at } X) \implies \vec{E}_1 = -\frac{p}{4\pi\varepsilon_0 r^3}\hat{j}$$

$$\vec{p}_2 = p\hat{j} \quad (\text{equatorial at } X) \implies \vec{E}_2 = -\frac{p}{4\pi\varepsilon_0 r^3}\hat{j}$$

$$\vec{E}_X = \vec{E}_1 + \vec{E}_2 = -\frac{p}{2\pi\varepsilon_0 r^3}\hat{j} \implies \text{(P)} \rightarrow \text{(2)}$$

Evaluating entry (Q):

$$\vec{p}_1 = p\hat{j} \quad (\text{equatorial at } X) \implies \vec{E}_1 = -\frac{p}{4\pi\varepsilon_0 r^3}\hat{j}$$

$$\vec{p}_2 = -p\hat{j} \quad (\text{equatorial at } X) \implies \vec{E}_2 = -\frac{-p}{4\pi\varepsilon_0 r^3}\hat{j} = \frac{p}{4\pi\varepsilon_0 r^3}\hat{j}$$

$$\vec{E}_X = \vec{E}_1 + \vec{E}_2 = 0 \implies \text{(Q)} \rightarrow \text{(1)}$$

Evaluating entry (R):

$$\vec{p}_1 = p\hat{j} \quad (\text{equatorial at } X) \implies \vec{E}_1 = -\frac{p}{4\pi\varepsilon_0 r^3}\hat{j}$$

$$\vec{p}_2 = p\hat{i} \quad (\text{axial at } X) \implies \vec{E}_2 = \frac{2p}{4\pi\varepsilon_0 r^3}\hat{i}$$

$$\vec{E}_X = \vec{E}_1 + \vec{E}_2 = \frac{p}{4\pi\varepsilon_0 r^3}(2\hat{i} - \hat{j}) \implies \text{(R)} \rightarrow \text{(4)}$$

Evaluating entry (S):

$$\vec{p}_1 = p\hat{i} \quad (\text{axial at } X) \implies \vec{E}_1 = \frac{2p}{4\pi\varepsilon_0 r^3}\hat{i}$$

$$\vec{p}_2 = p\hat{i} \quad (\text{axial at } X) \implies \vec{E}_2 = \frac{2p}{4\pi\varepsilon_0 r^3}\hat{i}$$

$$\vec{E}_X = \vec{E}_1 + \vec{E}_2 = \frac{p}{\pi\varepsilon_0 r^3}\hat{i} \implies \text{(S)} \rightarrow \text{(5)}$$