List-I shows four configurations, each consisting of a pair of...

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

2 r

apart along the

x

direction. The midpoint of the line joining the two dipoles is

X

. The possible resultant electric fields

\vec{E}

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.

		List-II
$(P)$	$(1)$	$\vec{E}=0$
$(Q)$	$(2)$	$\vec{E}=-\frac{p}{2 \pi \epsilon_0 \mathrm{r}^3} \hat{\mathrm{j}}$
$(R)$	$(3)$	$\vec{E}=-\frac{p}{4 \pi \epsilon_0 \mathrm{r}^3}(\hat{\mathrm{i}}-\hat{\mathrm{j}})$

$(S)$	$(4)$	$\vec{E}=\frac{p}{4 \pi \epsilon_0 \mathrm{r}^3}(2 \hat{\mathrm{i}}-\hat{\mathrm{j}})$
	$(5)$	$\vec{E}=\frac{p}{\pi \epsilon_0 \mathrm{r}^3} \hat{\mathrm{i}}$

Options

A $\mathrm{P} \rightarrow 3, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 2, \mathrm{~S} \rightarrow 4$
B $\mathrm{P} \rightarrow 4, \mathrm{Q} \rightarrow 5, \mathrm{R} \rightarrow 3, \mathrm{~S} \rightarrow 1$
C $\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 4, \mathrm{~S} \rightarrow 5$
D $\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 3, \mathrm{~S} \rightarrow 5$

C. $\mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 4, \mathrm{~S} \rightarrow 5$

E_{\text{net }}=\frac{-2 k P}{r^3} \hat{j} E_{n e t}=\frac{-P \hat{j}}{2 \pi \epsilon_0 r^3} \mathrm{E}_{\mathrm{net}}=0 \frac{2 \mathrm{P} \hat{\mathrm{i}}}{4 \pi \epsilon_0 \mathrm{r}^3}-\frac{\mathrm{P} \hat{\mathrm{j}}}{4 \pi \epsilon_0 \mathrm{r}^3} \mathrm{E}_{\mathrm{net}}=\frac{4 \mathrm{kP} \hat{\mathrm{i}}}{\mathrm{r}^3} \mathrm{P} \rightarrow 2, \mathrm{Q} \rightarrow 1, \mathrm{R} \rightarrow 4, \mathrm{ S} \rightarrow 5

Ans. (C)