Question

List Match Set-I

In each situation of Column - I, two electric dipoles having dipole moments $p_1$ and $p_2$ of same magnitude (that is, $p_1=p_2$) are placed on $x-$axis symmetrically about origin in different orientations are shown. In Column - II certain inferences as drawn fro these two dipoles. Then match the different orientations of dipoles in Column - I with the corresponding resulting in Column – II

	Column-I		Column-II
(A)	(${\overrightarrow{P}}_1\text{and}{\overrightarrow{P}}_2$ P2are perpendicular to x-axis as shown)	(P)	The torque on one dipole due to other is zero.
(B)	(${\overrightarrow{P}}_1\text{and}{\overrightarrow{P}}_2$ are perpendicular to x-axis as shown)	(Q)	The potential energy of one dipole in electric field of other dipole is negative
(C)	(${\overrightarrow{P}}_1\text{and}{\overrightarrow{P}}_2$ are Parallel)	(R)	There is one straight line in x-y plane (not at infinity) to x-axis as shown which is equipotential
(D)	(${\overrightarrow{P}}_1\text{and}{\overrightarrow{P}}_2$ are perpendicular to x-axis as shown)	(S)	Electric field at origin is zero.

Which of the following option has the correct combination considering column-I and column-II

Answer 1

The electric field due to one dipole at centre of other dipole is parallel to the dipole in all cases. Hence, torque on dipole is zero in all cases.
In cases (ii) and (iii), the electric field at second dipole due to first is along the second dipole, hence electrostatic potential energy of second dipole is negative.
In cases (i) and (ii), x-axis is the line of zero potential.
In case (iii), y-axis is the line of zero potential. In cases (ii) and (iv), electric field at origin is zero.