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 configur

Question

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 $E$ 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.

		List-II
$(P)$	$(1)$	$E = 0$
$(Q)$	$(2)$	$E = - \frac{p}{2 π ϵ _{0} r ^{3}} \hat{j}$
$(R)$	$(3)$	$E = - \frac{p}{4 π ϵ _{0} r ^{3}} (\hat{i} - \hat{j})$

$(S)$	$(4)$	$E = \frac{p}{4 π ϵ _{0} r ^{3}} (2 \hat{i} - \hat{j})$
	$(5)$	$E = \frac{p}{π ϵ _{0} r ^{3}} \hat{i}$

Options:

Answer:

C

Solution:

$E_{net} = \frac{- 2 k P}{r ^{3}} \hat{j}$

$E_{n e t} = \frac{- P j ^}{2 π ϵ _{0} r ^{3}}$

$E_{net} = 0$

$\frac{2 P i ^}{4 π ϵ _{0} r ^{3}} - \frac{P j ^}{4 π ϵ _{0} r ^{3}}$
$E_{net} = \frac{4 kP i ^}{r ^{3}}$ $P \to 2, Q \to 1, R \to 4, S \to 5$ Ans. (C)

TestHub · Accepted Answer

E net ​ = r 3 − 2 k P ​ j ^ ​ E n e t ​ = 2 π ϵ 0 ​ r 3 − P j ^ ​ ​ E net ​ = 0 4 π ϵ 0 ​ r 3 2 P i ^ ​ − 4 π ϵ 0 ​ r 3 P j ^ ​ ​ E net ​ = r 3 4 kP i ^ ​ P → 2 , Q → 1 , R → 4 , S → 5 Ans. (C)

Physics - Electrostatics Question with Solution | TestHub

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