JEE Advanced 2025 Paper 1 · Q14 · Magnetic Dipole & Moment

Question

List-I (above) 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:

(1) $\vec{E} = 0$
(2) $\vec{E} = -\dfrac{p}{2\pi\epsilon_0 r^3}\hat{j}$
(3) $\vec{E} = -\dfrac{p}{4\pi\epsilon_0 r^3}(\hat{i}-\hat{j})$
(4) $\vec{E} = \dfrac{p}{4\pi\epsilon_0 r^3}(2\hat{i}-\hat{j})$
(5) $\vec{E} = \dfrac{p}{\pi\epsilon_0 r^2}\hat{i}$

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

SolveKar AI · Accepted Answer

Let $E_0=\dfrac{p}{4\pi\epsilon_0 r^3}$. At distance $r$ on a dipole's axis the field is $2E_0$ along $\hat p$; on its broadside it is $E_0$ opposite to $\hat p$.

(P) Both dipoles $\parallel \hat j$, on $x$-axis. $X$ lies on each one's broadside: each gives $-E_0\hat j$, total $-2E_0\hat j = -\dfrac{p}{2\pi\epsilon_0 r^3}\hat j$ → (2).
(Q) Anti-parallel ($+\hat j$ and $-\hat j$): broadside fields cancel, $\vec E=0$ → (1).
(R) One dipole $\hat j$ (broadside at $X$, gives $-E_0\hat j$), one dipole $\hat i$ (axial at $X$, gives $+2E_0\hat i$). Sum $=E_0(2\hat i-\hat j)=\dfrac{p}{4\pi\epsilon_0 r^3}(2\hat i-\hat j)$ → (4).
(S) Both dipoles axial $+\hat i$ on opposite sides of $X$: each gives $+2E_0\hat i$, total $4E_0\hat i=\dfrac{p}{\pi\epsilon_0 r^3}\hat i$ → (5).

Match: P→2, Q→1, R→4, S→5 → option (C).

JEE Advanced 2025 Paper 1 · Q14 · Magnetic Dipole & Moment

Solution